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Full text of "Tables for azimuths, great-circle sailing, and reduction to the meridian, with a new and improved "Sumner" method: latitudes 90 N. to 90 S., declinations 90 N. to 90 S. : also other useful navigational tables, with numerous examples of double altitudes, equal altitudes, azimuths, etc."

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$B 72 mi 



FOURTH EDITION, 1916. 



. S. BLACKBURNE. 



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TA B L ES 

FOR 

AZIMUTHS, GREAT-CIRCLE SAILING, 

AND 

REDUCTION TO THE MERIDIAN, 

WITH A 

NEW AND IMPROVED "SUMNER" METHOD: 



LATITUDES - - 90 N. TO 90 S. 

DECLINATIONS 90 N. TO 90 S. 

4muths through Tables A, B, and C (or separately through Table D) for all the Heavenly Bodies 
at any Time the Body is above the Horizon; and Great-circle Sailing-courses for all Latitudes. 



Also other Useful Navigational Tables, with Numerous Examples of 
Double Altitudes, Equal Altitudes, Azimuths, &c. 



H S. BLACKBURNE (Extra Master), 

Principal Examiner of Masters and Mates in^ New Zealand, and Nautical Adviser to the Government. 



PUBLISHED BY DIRECTION OF THE HON. THE MINISTER OF MARINE. 




WELLINGTON, N.Z. 
BY AUTHORITY: MARCUS F. MARKS, GOVERNMENT PRINTER, 



LOUIS WEULE CO, 

autical Instruments 



BOOKS ON N A V1GATION, ETC. 

AGENCY FOR 

U.S. GOVERNMENT CHARTS AND PUBLICATIONS 



PREFACE. 



THE tables and problems here published are a reprint, for the most part 
of the azimuth tables which have been published in the first three years' 
issues of the " New Zealand Nautical Almanac." 

Tables D and G are now reprinted and brought up to date from the 
writer's original tables published in 1883, an d Tables A, C, and D have 
been extended from 60 to 85 of latitude. This will meet the needs 
of Arctic and Antarctic explorers, as well as the traders to such places 
as Archangel. Some years ago the writer promised Captain Liddle, 
who was then trading to Archangel, that he would extend his tables 
to latitude 72 to meet the needs of those trading in these high 
latitudes, outside the limits of the ordinary azimuth tables. With 
this extension they now constitute the most complete and comprehen- 
sive azimuth tables yet submitted to the seafaring community, giving 
with great simplicity sufficient accuracy to meet even the requirements 
of the extra-masters' examination. By the aid of Tables A, B, and C 
(when the hour-angle is known) the true bearing of the sun, moon, 
planets, and fifty-one of the brightest stars may be found in a couple 
of minutes at any hour of the day or night by the use of only about 
half a dozen figures. 

As requests have been made from candidates for examination for 
permission to use these A, B, and C tables for solving some of the pro- 
blems in the examination for masters and mates, and recommendations 
have been made for their use in the local examinations in New Zealand, 
these tables are now published separately, and, for the sake of giving the 
azimuth with greater precision for examination purposes, the factors are 
given in Tables A and B to three places of decimals when hour-angles are 
between four and eight hours, except in the very high latitudes, where 
so many decimals are unnecessary. 

The comprehensiveness of the A, B, and C tables for azimuth pur- 
poses is simply marvellous. They cover only forty-two pages, and give 
not only all the azimuths of the above-mentioned heavenly bodies com- 
prised in the four large tables of inspection (which cover several hundred 
pages), but also a considerable number of azimuths which are outside 
the limits of the larger tables. They are therefore especially valuable 
for use in the " Sumner " and " double altitude " problems, where the 
large azimuth tables omit to give the azimuth when the body is near 
either the upper or lower meridian. It was this omission (which is 
especially felt in low latitudes) which first led the writer to calculate 
and publish his original A and B azimuth tables. When the price of 
the large azimuth tables is taken into consideration (Burdwood's and 
Davis's for the sun, and Davis's and Goodwin's for the higher-declination 
stars), amounting altogether to fi 135, the boon to navigators in the 



380032 



IV 



price only, apart from the much greater extent of limit comprised in these 
small tables, must, I think, be recognized and appreciated by those who 
have only moderate means. 

In the writer's old A and B tables the factors throughout were 
given to three places of decimals for the sake of being able to show that 
these tables would give the azimuth as accurately as the large tables of 
inspection. He has, however, often regretted having given the three 
places of decimals in the smaller hour-angles, as it makes interpolation at 
sight more difficult, and the azimuth is obtained with sufficient accuracy 
for practical purposes without it. In this edition three places of decimals 
have been given wherever necessary to give sufficient accuracy for ex- 
amination purposes. Even in the Board of Trade extra-masters' exami- 
nation any azimuth tables which give the azimuth correctly within half 
a degree may be used in the time-azimuth problem. These tables will 
nearly always give the azimuth correctly within 0*1 of the truth. To 
insure the most rigid accuracy in the second place of decimals, whenever 
the third place of decimals in the writer's old table came to 5 a fresh 
calculation has been made. In the parts where three places of decimals 
have been given, new calculations have been made and compared with 
the old tables. 

In Table B all the stars not less bright than ro magnitude have been 
computed separately for their actual declinations for the epoch 1910 ; 
and, as their annual change of declination is so small, these factors will 
be sufficiently accurate for all practical purposes for the next thirty or 
forty years, and no interpolation for declination will be needed. 

The whole of Table C has been newly calculated on the lines of the 
late Mr. W. H. Rosser's table published in " Node's Epitome," but this 
table (including latitudes to 85) contains more than eight times the 
number of his computations, for the sake of giving greater accuracy and 
less interpolation. This plan will, I believe, be more popular with most 
navigators than that previously given in the writer's old table, as the 
azimuth is taken out more directly, and quite accurately enough for all 
practical purposes. 

Tables A and B have been worked to five places of decimals where 
necessary, and Tables C and C 2 , though only given to the nearest decimal 
of a degree, have been calculated throughout to the nearest decimal of a 
minute for the sake of accurate checking by differences. 

Table D has also been checked from the writer's old calculations, 
and, where necessary, seven-figure logarithms have been used to deter- 
mine fine points ; otherwise, with the exception of changed heading and 
the addition of two pages, giving latitudes from 61 to 85, it remains the 
same as when first published in 1883. 

Table A, from latitude 61 to 82, was calculated with great care 
by Captain Thomas Liddle, who very kindly sent to the writer the 
whole of his work. This was carefully compared by the writer with 
his own calculations. Throughout the compilation of the whole of these 
tables such minute care has been taken and rigid accuracy aimed at 
that the writer has good reason for believing that not one factor in a 
thousand will be found in the slightest degree in error. 

An important feature in this work, which the writer believes he 
was the first to introduce, and which should prove a boon to navigators, 



is the method here presented of working the " Sumner " problem on a 
plane chart in connection with these tables. This method is much 
shorter than that usually taught in the navigation schools in prepara- 
tion for the Board of Trade examinations, and at the same time it gives 
greater accuracy, especially when the plan which is here advocated 
is adopted, of combining the ex-meridian and chronometer observa- 
tions when one of the bodies observed is near the meridian ; and it 
has the great advantage of only requiring one chart, instead of having 
to carry about " Sumner " charts for every change of latitude N. and S. 
of the Equator. The Marine Department of the New Zealand Govern- 
ment has published some very accurate charts on a convenient scale for 
this purpose. 

As the request from the New Zealand Government to the Board of 
Trade to allow the use of these tables, and improved " Sumner " method 
for solving the " Sumner " and " double altitude " problems, in the New 
Zealand examination for masters and mates was not granted, two ex- 
amples have been clearly worked and plotted on the chart (see pages 104 
and no) one of two observations of the sun as given in the masters' 
and mates' examinations, and the other of observations of two different 
stars as given in the extra-masters' examination. These examples illus- 
trate the possible errors that may arise from the old method. This 
error is especially aggravated in low latitudes, where in the summer 
months one of the altitudes must always be great, and often within 
half an hour of the meridian. The error in such cases would sometimes 
amount to 6 or 7 minutes of latitude. The summer months, too, in these 
latitudes are generally the rainy season, when double altitudes are most 
needed. We trust that after further perusal and trial of these tables 
and the methods here advocated the Board of Trade may see fit to alter 
their decision, especially as the tables are now printed separately from 
the " New Zealand Nautical Almanac." 

Although the examples above mentioned are purposely exceptional 
ones, for the sake of better illustration, smaller errors will often arise if 
the method at present used by the Board of Trade for the masters' and 
mates' examinations is always adopted. Many an opportunity of deter- 
mining the ship's position is lost owing to the impression among many 
navigators that the " Sumner " method is not of value when one of the 
observations is within, or a little outside of, the ordinary ex-meridian 
limits. At other times a false confidence is encouraged about the accu- 
racy of the ship's position by trusting too implicity to the latitude by 
ex-meridian following a chronometer observation for longitude, without 
due regard to the bearing when the first observation was taken. 

An example from " Norie's Navigation " (the best-known epitome of 
navigation in the world) will illustrate both these contentions. On pages 
368 and 369 of the 1900 edition an example is given of a longitude by 
chronometer at 8 h. 45 m. a.m., and an ex-meridian at n h. 30 m. a.m. 
At the close of the work the editor says, " Since by reference to the 
table, page 309, the hour-angle of the second observation is within the 
limits of the reduction to the meridian, it follows that the latitude found 
will be the correct latitude, unless the latitude and longitude used in the 
calculation are both very erroneous." He seems to have ignored the 
fact that when the first observation was taken the sun was not on, or 
even near, the prime vertical (and never is in the winter months in high 

Inset Azimuth. 



VI 

latitudes), and therefore the time resulting from this observation was 
more than I minute in error ; and, although the sun was only 8J from 
the meridian when the second observation was taken, the resulting posi- 
tion was over 2' in error in the latitude and about 2\' in error in the 
longitude from the position given, and which the reader might naturally 
infer was correct. The editor afterwards goes on to say that " if the 
second observation had not been within the limits of the table on page 309, 
and the azimuth had been small, or if the estimated latitude and longi- 
tude had been very erroneous, neither the latitude nor the longitude could 
have been found with any degree of accuracy by the ordinary methods. 
Now what is termed the ' new navigation ' may prove useful." As this 
closes the chapter in " Norie " on the " Sumner " method, in which is 
included the above-mentioned example of finding position by chrono- 
meter longitude and an ex-meridian, it is presumed that these are what 
are referred to as the " ordinary methods." 

Now, the author maintains that if the " Sumner " method is dealt 
with in a practical way, either as advocated in these pages by numerous 
examples, or as given in the " American Practical Navigator," by Bow- 
ditch, revised by Lieut. G. W. Logan, U.S. Navy, the " Sumner " posi- 
tion will give quite as accurate results as by the method which is termed 
the " new navigation," and he ventures to believe that this method, too, 
will be easier for most men to grasp. He guarantees that he will take 
any of the double-altitude or simultaneous-altitude problems out of the 
numerous examples given in Captain Thompson's " Navigation Simpli- 
fied " (which we may presume are fair specimens of the problems given 
at the Board of Trade examinations) and by the methods here pre- 
sented, by the aid of these tables, either with or without the aid of 
chart, will find the position of ship with similar accuracy to that ob- 
tained by the most rigorous methods of trigonometry, and well within 
the limit of accuracy required in the extra-masters' examination. His 
contention is that the papers set in the examination-room should above 
all things tend to make men better practical navigators, and he believes 
that any impartial judge must admit that the methods advocated in 
these pages for the " Sumner " problem are superior in many points to 
that which is at present encouraged by the Board of Trade examinations. 
The advantages may be thus summarized : (i) Greater accuracy ; 

(2) fewer figures, and consequently less time required for the work ; 

(3) one chart does for any navigable latitude ; and (4) many observa- 
tions which would be considered useless for the ordinary " Sumner " 
give excellent results with even fewer figures by combining ex-meridian 
and chronometer observations together, as illustrated in this work by 
various examples. Most officers pass the examination for master many 
years before they get command, and it is hardly to be expected that they 
will keep a supply of " Sumner " charts for the various latitudes that 
they trade in ; consequently the practice of this method, which they 
have learnt for their examination, is sure to be neglected. The writer, 
speaking for himself, can testify that he never used it at sea, though, 
much to his regret, for more than ten years he has had to teach it or 
examine candidates in their knowledge of it. 

Very shortly after the publication of the writer's first edition of the 
A_and B azimuth tables the late Mr. W. H. Rosser published abridged 
A7 B, and C tables for the same purpose, and afterwards slightly ex- 



Vll 

tended them for publication in " Node's Epitome." They are excellent 
tables, and very concise, but even as enlarged in " Norie " require in 
most places considerable interpolation, the time-interval being sometimes 
20 minutes and 30 minutes apart, which naturally could not admit of as 
much accuracy as a fuller table. A few years later Captain Lecky asked 
and obtained the writer's permission to publish the A and B azimuth 
tables in his famous " Wrinkles." Captain Lecky then extended and 
improved them, and later on published them in a separate book with 
further extensions and improvements, showing how the tables can be 
used for quite a number of navigational problems. 

In closing, the author has much pleasure in acknowledging the kind 
help voluntarily tendered to him by Captain Thomas Liddle, and in 
thanking him for his disinterested labours in the calculation of much of 
the extension of these tables. But for his perseverance in continuing to 
urge the writer to extend his tables it is very improbable that they would 
ever have been published in their present revised form. He would also 
like to thank the Hon. Mr. Hall- Jones, Minister of Marine, and the New 
Zealand Government for valuable clerical assistance in the compilation of 
a portion of these tables, for the confidence they have reposed in him. 
and for their liberality and public spirit in the interest of navigation all 
over the world in thus publishing an extension of navigational tables far 
beyond the limits of New Zealand's own trade. 

H. S. BLACKBURNE. 
April, 1905. 



Vll 



PREFACE TO FOURTH EDITION. 



SINCE the publication of the first edition of these tables in New Zealand 
by the New Zealand Marine Department the work has more than doubled 
in size, and the additional pages have no doubt increased the value and 
usefulness of the work. 

At the request of the Commander and Navigating Lieutenant of 
the British Antarctic Expedition s.s. " Terra Nova," the limits of the 
A and B Tables have been further extended so as to include all latitudes 
and declinations between the terrestial and the celestial North and 
South Poles. The tables are thus made available for azimuth, great- 
circle sailing, and reduction to the meridian for every part of the globe, 
and for every star in the heavens. 

A Traverse Table and Table C 1 have been added giving the azimuth 
to the nearest minute of arc up to 45 from the meridian for use 
when special accuracy is required in conjunction with the Ex-meridian 
Table.5 

This table, given to the decimal of a degree, was used in the author's 
original A and B Azimuth Tables published in 1883. 

Table D has been extended to comprise all latitudes between 85 N. 

and 85 S. 

Mr. H. B. Goodwin, R.N., formerly Examiner at the Royal Naval 
College, Greenwich, has drawn the writer's attention to the value of 
this table as an azimuth table, when both altitude and time are given, 
and he has in this edition given Mr. Goodwin's rule, and an example 
for using it in this direction, as well as explaining the purposes for 
which it was first calculated. 

The possessor of the book can make his own choice as to whether 
he uses Table D or Tables A, B, and C in the calculation of azimuths. 
Probably he will find D the handiest when the body is near the meridian, 
and (as its accuracy depends principally on the altitude) it will give a 
more accurate azimuth than the time-azimuth tables when the D.R. 
latitude used in the calculation of the time azimuth is incorrect, while 
the other tables will certainly give greater accuracy, without any 
uncertainty as to the naming of the azimuth, when the body is near the 
prime vertical. 

It is not, therefore, recommended that Table D should be used for 
azimuth purposes when the object of observation is too near the prime 
vertical, as close accuracy cannot then be expected, and there will then 
be uncertainty as to the naming of the bearing. 



IX 

A further extension and improvement on the Ex- meridian 
Table No. i has been made giving the reduction to the meridian 
with high altitudes up to 45 from the meridian. 

This table, as well as Ex-meridian Table No. 2, were published in 
1908 for use in conjunction with the A and B Tables. Although the 
tables only comprise a few pages they cover wider limits of use than 
most other ex-meridian tables, being available for every degree of 
latitude and declination from Pole to Pole, and they are equally avail- 
able for below-Pole, as for above-Pole observations. 

The table for correction of sun's and star's altitude has been extended 
for heights from 6 ft. to 80 ft. 

The table giving the apparent times of the meridian passages of the 
principal fixed stars has been calculated with great care for the year 
1910 (midway between two leap years), so that for any year for some 
time to come the error will not amount to more than about two minutes, 
with the single exception of Star Polaris, which has an increasing change 
in R.A. of nearly 29 sec. 

In this table the times of inferior as well as the superior transits of 
no less than forty-five of the circumpolar stars are given. 

This should be a great boon to navigators, as (so far as the author 
knows) no other navigational works give the times of star's meridian 
passages at the inferior transit, notwithstanding the special value of the 
below-Pole star for determining latitudes, on account of its slow motion 
in altitude and azimuth. 

A small table comprising two pages has been added after the 
ex-meridian table showing the error in latitude by ex-meridian due to 
4 seconds of error in the time. This table is especially useful in facili- 
tating work in connection with the problem of finding the position of 
ship from two ex-meridians or one ex-meridian and a chronometer 
observation, and quite dispenses with any need of a chart. 

A year or two ago the Board of Trade sanctioned the use of these 
tables for the time-azimuth problem in the New Zealand examination- 
rooms for candidates for foreign-going certificates for masters and mates, 
and already the great majority of the New Zealand candidates use them 
in preference to Burdwood's and Davis's Tables. 

Even naval officers after a very short trial of our tables have written 
to the author expressing their preference for them to the larger tables 
which are in general use in the Navy, quite apart from the fact of their 
far greater limits of use. 

I would again respectfully urge the Board of Trade to allow the 
use of our tables to candidates in the examinations for masters and 
mates in other countries, at least in Canada, where much of the Canadian 
coast-line is outside the latitude limits of the tables which they are 
obliged to use in the examinations. 

It is a matter of regret, and has been much commented on, that, 
owing to New Zealand having to comply with Board of Trade Regula- 
tions in respect to certificates for foreign-going vessels, we are still 



unable to use in our examinations the methods and navigational tables 
which we have compiled, at much labour and cost, for facilitating various 
problems in navigation, notwithstanding that the methods advocated 
in this work and assisted by the tables published herein give proof of 
much greater accuracy in the problem of determining the ship's position 
from two observations of the sun out of the meridian than by the 
method which we are obliged to use in our examinations to comply 
with the Board of Trade Regulations. 

The use, too, of the plane chart in the Sumner problem, which has 
been such a boon to the few who know about it, is still precluded from 
use in the examinations, and consequently it will take many years 
before the bulk of navigators know the advantages of it. 

HAROLD S. BLACKBURNE. 
Wellington, New Zealand, 
June, 1916. 



XI 



TABLE OF CONTENTS. 



Preface . . . . . . . . . . . . . . . . i_ x 

Explanation of Tables . . . . . . . . . . . . . . j_6 

Mean Places of 108 of the Brightest Stars for January, 1917 ; . . . . 7-8 

Apparent Times of the Meridian Passages of the Principal Fixed Stars . . g-n 

Tables A and B : Latitudes and Declinations 89 J -N. to 89^ S. . . . . 12-37 

Table C : Azimuths corresponding to A and B Correction ; Latitudes 85 N 

to8 5 S. .. ,. 38-57 

Traverse table : Showing Difference of Longitude and corresponding 

Departure .. .. .. .. .. .. .. 58-67 

Table C 1 : Azimuth corresponding to A and B Correction in Departure , . 68-74 

Table C 2 : Position-lines corresponding to the A and B Correction for Use with 

the Plane Scale Chart in the " Sumner " Problem . . . . . . 75 

Table D : Showing the Error produced in the Time or Longitude by an Error 

of i ' in the Altitude ; Latitudes 85 N. to 85 S. . . . . . . 76-85 

Table E : Correction of Sun's and Star's Altitudes .. .. .. 86-87 

Table G : Star Polaris Azimuth Table . . . . . . . . . . 88 

Reduction to the Meridian of # Polaris . . . . . . . . . . 89 

Diagram to Aid in finding the Position of South Pole . . . . . . 90 

General Remarks on the Double-altitude and " Sumner " Problem .. .. 91-92 

Rule for finding the Position of Ship from Two Observations of Sun or Stars, 

with Example . . . . . . . . . . . . . . 92-96 

Remarks on the Position-line and " Sumner " Problem in connection with Ex- 
meridians . . . . . . . . . . . . . . . . 97 

Latitude by Ex-meridian when outside Ordinary Limits : Formula, Figure, and 

Examples . . . . . . . . . . . . . . . . 97-99 

Examples of Double-altitude Position by Two Sun Observations . . . . 100-103 

Example of the " Sumner " Problem as given in the B. of T. Examinations . . 104 

Example showing Use of Tables A, B, and C 2 in working the "Sumner" 

Problem ,. .. .. .. .. .. .. .. 105 

Example to show Method of plotting the True Line of Position or Circle of 

Altitude by Aid of the A and B Tables . . . . . . . . 106 

Example of Double-altitude Position by Two Stellar Observations . . . . 107-109 

Simultaneous Observations of Two Stars by the Old " Sumner " Method . . no 

Simultaneous Observations of Two Stars by the Improved " Sumner " Method 111-112 

The Superiority of Stellar over Solar Observations .. .. .. 113 

Diagram and Examples to illustrate how Errors of Altitude may be eliminated 

by Observations of Three Stars .. .. .. .. .. 113-115 



Xll 

Pages 
Examples to find Stars suitable for determining Position by Double Altitudes 116 

Examples of finding Ship's Position by Simultaneous Observations of Sun and 

Moon .. .. .. .. . .. .. .. 117-118 

Examples of finding the True Bearings of Sun, Moon, and Stars ; also the 
Error and Deviation of the Compass, and the Great-circle Courses of the 
Globe .. .. .. .. .. .. .. .. 119-122 

Illustrations to show how Lives and Ships may be saved by the Careful 

Observer, and, conversely, how Lives may be lost . . . . . . 122-124 

Example of finding the Error of Chronometer by Observations in Artificial 
Horizon, showing the Use of Table D in working out several Observations 
separately.. .. .. .. .. .. .. .. 125 

Remarks on the Value of Equal Altitudes at Sea, with Examples . . . . 126-128 

Remarks on Ex-meridian and Meridian Altitudes . . . . . . . . 129-131 

A few Navigational Notes and Cautions .. .. .. .. .. 131-134 

Some Simple Methods (including Diagram and Table H) for finding the Ship's 
Distance from a Point by Two Bearings and the Run in Interval between 
them .. .. .. .. .. .. .. 135-139 

Explanation of the Diagonal Scale and Protractor, and Remarks on the 

Pelorus .. .. .. .. .. .. .. .. 139-140 



SUPPLEMENTARY EX-MERIDIAN TABLES. 

Explanation of Tables .. .. .. .. .. .. .. 142-143 

Table showing Limits of Ex-meridian Table No. i . . . . . . 144 

Ex-meridian Table No. i .. .. .. .. .. .. 145-151 

Table showing Limits of Ex-meridian Table No. 2 . . . . 152 

Ex-meridian Table No. 2 . . . . . . . . . . . . 153-155 

Table M : Showing the Error in Latitude due to an Error of Four Seconds in 

Time or i ' of Longitude .. .. .. .. .. 156-157 

Examples of finding the Position of Ship from Two Sun Ex-meridian Observa- 
tions, using Ex-meridian Tables, and Accuracy of Position also proved . . 158-162 

Example of finding Ship's Position from Ex-meridian and Chronometer 

Observations of Sun and Moon . . . . . . . . . . 163 

Example of finding Ship's Position from Combined Ex-meridian Observations 

of Two Stars, and same Example worked from Two Calculated Longitudes 164-165 

Example of finding Ship's Position from Two Observations of Sun and Planet 

Venus, Longitude and Ex-meridian Observations . . . . . . 166 

Position of Ship from Two Stellar Observations combining Chronometer 

Longitude Observation with an Ex-meridian below the Pole . . . . 167 

Example to find Approximate Altitudes and Bearings of suitable Stars for 

Observation to quickly obtain Position of Ship . . . . . . 168 

Example of finding Ship's Position from Two Calculated Ex-meridian 

Latitudes Four Hours from Meridian below the Pole . . . . . . 169 

Example of finding Ship's Position from Ex-meridian, Position-line, and 

Soundings.. .. .. .. .. .. .. .. 170 

Formula for Calculation of Latitude and Altitude . . . . . . 171 

Advertisements .. .. .. .. .. .. .. 173-181 



EXPLANATION OF TABLES. 



The A, B, and C Azimuth Tables. 

TABLES A and B are used in combination (i) for finding the error of the longitude 
due to an error of one minute (i') of latitude, and (2) by the aid of Table C to find the 
azimuth or true bearing of celestial objects. 

Enter Table A with the hour-angle and latitude, and Table B with the hour-angle and 
declination, naming the factors taken from these tables according to the following 
rule: 

For Table A When hour-angle is less than 6 hours, name the factors taken from 
this table contrary to name of latitude. 

When hour-angle is greater than 6 hours, name the factors taken from Table A the 
same as the name of the latitude. 

For Table B Always name the factors taken from Table B the same as the name 
of declination. 

Add like and subtract unlike names. The sum or difference then of the factors 
from A and B will be the difference of longitude correction due to i' of error in the 
latitude. The correction must be named according to the name of the greater factor. 

The direction of this longitude correction (or the position-line, as it may be 
termed) is found by keeping the name thus obtained, and reversing the name of the 
object's bearing E. or W. of meridian. 

For the Azimuth With the A and B cor. thus found and named, enter Table C with 
the latitude and this cor. ; the corresponding azimuth is then taken out direct, and is 
given to the nearest decimal of a degree. It is named N. or S. according to the name 
of the cor., and East or West as the hour-angle is east or west of the meridian. The 
azimuth with these tables never exceeds 90, This saves the trouble (which also 
confuses some when using the large azimuth tables) of having to subtract the azimuth 
taken out from 180, and change the name of azimuth. 

For examples in use of the table see pages 119 and 120, and for great-circle 
sailing page 121. 



Traverse Table and Table C 1 . 

For the Azimuth when greater accuracy is required. When using the azimuth table to 
assist in the reduction to the meridian it is important to take out the azimuth with 
greater precision than is necessary under ordinary circumstances for compass- 
correction or position-lines. For this purpose a traverse-table (pages 58-67) and 
Table C 1 (pages 68-74 are used as follows : 

Rule. Turn the A B ( = difference of longitude correction) into departure by the 
traverse table, and take out the azimuth corresponding to the factor from the azimuth 
Table C 1 . The azimuth in this table is given to the nearest minute of arc for 45 from 
the meridian. 

EXAMPLES : To FIND THE AZIMUTH. 

(i.) Lat. 41 3 S. } (p. 20) A -274 S. 

O'sDecl. 23-58. I (p. 21) B "455S. 

H.A. 7h. lorn. W. j (p. 43) C -729 S. gives Az. S. 61-2 W. 
i Azimuth. 



(2.) Lat. 43 30 S. ) (p. 20) A -452 N. (p. 63) ro - 725 

* a Centauri S. I (p. 21) B 1-955 S. (p. 60) -503 = -365 

H.A. 4h. i8m. j D, long. 1-503 Dep. 1-090 

= Dep. 1-090 gives Az. (C 1 , p. 69) S. 42 32'. 

For further examples see pages 119-120, and on page 121 for great-circle sailing- 
courses. 



FORMULAE USED IN THE CALCULATION OF THE TABLES. 
A = tang of latitude x cotang of hour-angle. 
B = tang of declination x cosec of hour-angle. 

For C "Azimuths," cot azim. = cor. x cos latitude, where cor. is the result of 
the sum or diff. of A and B. 

For C 1 "Azimuths," cotan azim. = correction. 

For C 2 " Position-lines," tan position-line = correction. 

INTERPOLATION. 

When it is deemed necessary to interpolate, this can usually be done at sight, 
except for the hour-angles up to the first hour from the meridian, and in a high latitude 
up to the second hour from the meridian. 

For Table A, when both time and latitude are nearly midway between that given 
in the table, interpolate diagonally ; for example, lat. 40 30', hour-angle 2h. 22 m., it 
will be seen at a glance that 1-20 is the correct factor. For Table B there is no 
appreciable difference in 4m. of time (except in the very small hour-angles), and it is 
therefore only necessary to interpolate vertically for the fraction of the degrees of 
declination. For the bright stars no interpolation is necessary even for the declination, 
as the declination of a star does not appreciably change for many years, and the factors 
are here calculated for the stars' declination corresponding to the year 1910. For both 
Tables A and B the interpolation of the small hour-angles up to i hour should be 
effected by dividing the quantity given at i m. by the number of minutes that the body 
observed is from the meridian. The variation to i' of latitude at oh. i m. is given to 
assist in the interpolation for the odd minutes of latitude, in case surveyors or others 
should require a very accurate azimuth. 

The following example will illustrate how the interpolation may here be 
effected : 

Lat. 40 36', H.A. o h. 10 m. : required the azimuth. 

Lat. 40 at o h. i m. A. = 192-3' var. to i' of lat. = 6-82" or 6-82' to i of lat. 
Cor. to 36' = + 4-1 

3 6' = 0-6 x 6-82' = 4-09' 
10 



Lat. 40 36' = 19-64 = from Table C Az. 3-8 

If greater accuracy is required, 19-64' x cos lat. 40 36' gives cot az. 3 50' . 

19-64' log 1-2931 
40 36' cos 9- 



3 50' cot 11-1735 



EXAMPLE TO FIND THE DIFFERENCE OF LONGITUDE DUE TO ERROR IN THE 

LATITUDE. 

In lat. by D.R. 16 30' N., hour-angle 2 h. 44m. E. and 0's declination 11 S., the 
longitude was found to be 40 50' E. Required the longitude, in latitude 16 38 N., 
the latitude previously worked with having been found to be 8' in error. 



A = -34' S- 
B = -30' S. 

Sum -64' S. to W. = cor. or error in the longitude due to 
Lat. found to be 8' N. of D.R. 8 i' of error in the latitude. 

Cor. to 8' of lat. .. .. 5-12' or 5' 7-2" S. to W. or N. to E. 



Lat. 16 30' N. gives long. 40 50 o E. 
Cor. due to 8' of lat. o 5 7 E. 



Lat. 16 38' N. gives long. 40 55 7 E. 



Knowing the error of longitude due to an error of i' of latitude, we have the 
means ready at hand of quickly determining both the latitude and longitude when two 
suitable observations have been taken of celestial objects. 

This may be effected either by plotting the two positions and position-lines on the 
chart, which is the ordinary " Sumner " problem (worked with only two instead of the 
usual four hour-angles), or the position may be found even more expeditiously by simple 
proportion. 

The actual trend of the position-line for plotting on the plane chart may be found 
from Table C' 2 , attending to the rule there given ; or, by subtracting the azimuth as 
found from Table C from 90, and reversing the name of the object's bearing, the true 
position-line will be found for plotting on a Mercator chart. 

Any single observation, whether on or near the meridian, or prime vertical, or any 
other bearing, simply gives a position as being somewhere on a line of bearing at right 
angles to the bearing of object. If a second observation is taken after the body 
has changed its bearing, or another body is observed at the same time having a 
different bearing, we get another line of position, and the intersection of the two 
position-lines will give the latitude and longitude of the observer. Without the trouble 
of putting the position on the chart, the same principle may be worked out by a 
little proportion sum. 

The three elements used in finding the time or longitude are latitude, altitude, and 
declination. If these three elements are correctly known, the same time or the same 
longitude will be found by every celestial body observed, whatever the bearing may be. 
If, therefore, the declination and altitude are correctly known, any difference of 
longitude found, resulting from the observation of different bodies (or the same body 
after an interval of time between the observations), must be due to error in the 
latitude. 

The error in longitude due to i' error of latitude is given by the A and B Tables. 
It becomes, therefore, a simple matter of proportion to find the correction to apply to 
the latitude used in finding the longitude. Say the longitudes resulting from the 
observation of two different stars are 15' apart, and with star No. i every i' north of 
latitude throws the longitude o'8' more to the east, with star No. 2 every i' north of 
latitude throws the longitude 1-2' more to the west, then every i' of error in the 
latitude will throw the longitudes 2' apart, and the error of latitude will be found by the 
proportion 2' d. long. : 15' d. long. : : i' lat. : 7^' lat. 

This would be represented on the chart by the accompanying figure. 

The writer has found the ship's position b sVPos" of shio 

this method many hundreds of times, and find -< .. 

that he gets a more accurate latitude in this wa 
than even by the meridian altitude, experience 
having shown that although an altitude may 
often be slightly in error, yet a correct difference 
in altitude is generally measured, or the same 

amount of error will generally be thrown into ^ 

both observations, and when this is the case (if (|) d long IS' (2) 

the observations are suitably chosen) small errors l 

in altitude practically make no difference in the latitude. Observations which ha v3 been 
taken in the quicksilver of two stars not near the meridian, or of two sun observations 
with a suitable interval of time between them, have generally given the latitude within 
o'i r of the truth, when taken where the position of places has been accurately known. 




Table C 2 . Position-lines. 

Table C 2 gives the position-lines corresponding to the A and B correction at any 
time for plotting on a plane scale chart. By the aid of this small table any one pos- 
sessing a protractor rule with the ordinary diagonal, or any other scale of inches, can 
plot the " Sumner " position in his sight-book with even greater accuracy than he could 
obtain it from the ordinary " Sumner " Mercator charts. The table does not give the 
true geographical lines of position, but lines of position which will give the same result 
as to latitude and longitude on a plane chart as the true lines of position would give on 
a Mercator chart. See instruction at foot of page under the table (p. 75). 



Table D. Altitude and Time-azimuth Table, showing the Error produced 
in the time or Longitude by an Error of 1' in the Altitude. 

This table gives best results for azimuth when body is near the meridan. It will 
not give accurate results when body is near the prime vertical, and there is then 
uncertainty as to naming the azimuth N. or S. of the prime vertical. 



Rule for finding the Azimuth. 

With H.A. as Az. and decl. as lat., go to Table D. 

Take out coefficient ; call it M. 

With alt. as lat. and M., take out Az. at top or side. 

EXAMPLE. 
Lat. 41 S. * Canopus (decl. 52 39' S.) H.A. 3h, lorn. 405. = 47 40'. Alt. 56 5'. 



47 



Required the Azimuth. 
8 ' 92 ' Lat < alt ') 5<5 5 '' and M ' 8 ' 9 * 



Table D will be found very useful in working out separately a set of observa- 
tions, both with artificial horizon and at sea ; or for working out another person's 
observations, taken within a few minutes of the same time. It also shows at sight the 
degree of dependence of any observation. And if at any time it is found that an 
erroneous altitude has been worked with, the longitude will readily be corrected by this 
table, a greater altitude giving a smaller hour-angle, or with A.M. sights a greater 
altitude making the longitude more to the eastward, and a lesser altitude making the 
longitude more to the westward vice versa with P.M. sights. 

It will also be found useful when taking time azimuths by the sun or stars (when 
altitude is low) for readily obtaining the correct hour-angle, as in the following 
example: Lat. 20 N., # Arcturus bearing N. 71 E. (true), altitude 5. Table D at 
lat. 20 and azimuth 71 gives 4-5 m. of time to i change of alt. Table 26 (Raper), lat. 
20 N., decl. 20 N., gives * 's hour-angle at rising or setting 6h. 30 m. 



*'sH.A. at 5 



The results of the table can be easily found by inspection from the traverse table. 
At the Equator, when the sun or any other heavenly body is on the prime vertical, it 
moves at the rate of i in 4 m., or i' in 4 s. of time ; and, in any other latitude, when the 
sun is on the prime vertical, the ratio of its movement will be dep. : diff. long. Having, 
then, the rate of movement in any latitude on the prime vertical, the rate of movement 
on any other bearing may be found by the traverse table. 

Example. In latitude 30, and O's bearing N. 63 E., required the rate at which 
it moves. In latitude 30, against 4 in D. lat. column, is 4-62 in dist. column ; with 
O's bearing 63, and 4^62 in dep. column, we have 5-18 in distance column = 5'i8s. to 
i' of altitude. 

The following formula was used in the calculation of the table: D = secant of 
latitude x cosecant of azimuth x 4. 

Further examples in the use of the table are given on pages 105 and 125. 



Table E. Altitude Corrections of Sun and Stars. 

This table (the upper half for the sun, and the lower half for the stars) gives the 
lump correction to apply to their observed altitudes, involving for the sun dip, refrac- 
tion, semidiameter, and parallax, and for the stars dip and refraction. 

As the correction for very small altitudes changes rapidly, a supplementary table 
is given on page 87 for the correction of both sun and stars, at a height of 40 ft. 
above sea-level, for altitudes between 3 and n, for every few minutes of altitude^ 
and for other heights greater or less than 40 ft. a second correction is given in same 
table. 

Heights are given from 6ft. to Soft, so as to meet the need of navigators in every 
class of vessel, from the smallest to the largest. As standard authorities still slightly 
differ in their dip and refraction tables, a mean of the dip and refraction given in the 
three standard works (Raper, Inman, and Norie) has been used in the calculation of 
the table here given, and great care has been taken to insure accuracy. 



Table P. Acceleration Table. 

This table is used for converting intervals of mean solar time into equivalent 
intervals of sidereal time. The seconds column which is given in most navigational 
tabular works has here been omitted for the sake of space, and because it is considered 
quite unnecessary in ordinary practical navigation. In practical navigation it becomes 
necessary in nearly all the problems where stars are used to convert mean solar time 
into sidereal time, as, for instance, in the time azimuth, longitude by chronometer, and 
the ex-meridian problems. In these problems the time is generally taken by a chrono- 
meter keeping mean solar time, and to compare this with the sidereal time found by the 
stellar observation it must be reduced to sidereal time. 

Examples will be found among some of the worked-out problems which follow the 
tables in this book. 



Table G. Star Polaris Azimuth Table. 

This table is useful especially in latitudes between 15 N. and 30 N., as, for 
instance, in the Red Sea. In a high latitude the altitude will be too high for compass- 
correction work, and it is not therefore given beyond 60 of latitude. 

Examples in the use of table are given later on in this book. 

The table has been calculated for stars' declination in 1910 viz., 88 49' 
33-57" N. 



The Mean Places of 108 of the Brightest Stars, in order of Right 
Ascension, for 1st January, 1917. 

On pages 7-8 the mean places of 108 of the brightest stars are given, in the order 
of their right ascension, for the ist January, 1917. In the column headed " Mag." the 
adopted unit of brightness is designated i'o. The magnitudes of stars are determined 
to tenths of a magnitude with reference to this adopted unit. The magnitudes of the 
ten stars brighter than the unit are indicated by figures less than i-o: thus, the value 
0-3 for Arcturus indicates that that star is seven-tenths of a magnitude brighter than 
the unit; the value 1-4 for Sirius that it is 2-4 magnitudes brighter than the unit. 
As the right ascensions and declinations of the stars do not change uniformly through- 
out the year, the correction for intermediate months cannot be made accurately by 
multiplying the annual change by a fraction of the year ; but the change is so small 
that for navigational purposes at sea the right ascensions and declinations here given 
may be used without appreciable error for azimuths and latitudes, and even for longitude 
the error due to using these elements would seldom exceed a mile. When accuracy is 
required the navigator should use the " Admiralty Nautical Almanac," where the right 
ascensions and declinations of these and many other stars are given very minutely for 
every ten days throughout the year. 



Approximate Apparent, Times of the Meridian Passages of the Principal 

Fixed Stars. 

The times are given in this table for the ist of each month, and the meridian of 
Greenwich. To find the time for any other day subtract the portion of time cor- 
responding to the day of the month in the day-correction table. Add i min. for every 
90 of east longitude and subtract i min. for every 90 of west longitude. 

The time of the meridian passage of each star has been carefully calculated to the 
nearest second of time, and is given in the table to the nearest minute. 

For the circumpolar stars which never set in higher latitudes than 50 N. or S. the 
times of the meridian passages of the inferior as well as the superior transit has been 
given. 

EXAMPLE AND CAUTION IN USING THIS TABLE. 

Required the meridian passage of * j8 Centauri on 3ist October, in longitude 
10 W. 

H. M. 

Mer. pass, of * ft Centauri on ist Oct. is i 30 p.m. 
Cor. for 3ist day i 52 

D. 

Approx. time 31 23 38 = n 38 a.m. on ist Nov. 

2nd cor. required 4 

D. 

Approx. mer. pass. * /3 Centauri 31 23 34 or n 34 a.m. on ist. Nov. 

The interval in this case is within 2 hours of 31 days instead of 30 days, therefore 
nearly 4 minutes more correction is required to be subtracted. The correction for longi- 
tude would be less than 10 seconds. 

The table is calculated for the year 1910, but will be within 2 min. for many 
years, with the single exception of the * Polaris which has an annual and increasing 
change in R.A. of over 273., and will therefore be about 5 min. later in passing the 
meridian in 10 years' time. 



Supplementary Ex-meridian Tables, &c. 

Explanations given on pages 142 and 143. 



THE MEAN PLACES OF 1O8 OF THE BRIGHTEST STARS 

IN ORDER OF RIGHT ASCENSION, 
FOR 1st JANUARY, 1917. 



Star s Name. 


Mag. 


Right 
Ascension. 


Annual I 
Change. 1 


Declination. 


1} 






H. M. S. 


S. 


O -1 It 




a Andromedae .. (Alpheratz) 


2'2 


o 4 5-6 


4-3-09 


N. 28 37 56 


+ 2CTO 


ft Cassiopeiae 


2'4 


4 44-4 


3-12 


N. 58 41 3i 


4-20-0 


a Phcenicis 


2- 4 


O 22 II'O 


2'95 


S. 42 45 25 


2O'O 


a Cassiopeiae . . (Schedar) 


Var. 


o 35 47-2 


3-38 


N. 56 4 56 


4-I9-8 


ft Ceti . . . . (Deneb Kaitos) . . 


2'2 


o 39 25-4 


3-00 


S. 18 26 31 


-19-8 


y Cassiopeiae .. 


2'3 


o 51 41-2 


+ 3'6o 


N. 60 16 3 


+ I9-5 


ft Andromedae . . (Mirach) 


2'4 


5 4-8 


3'34 


N. 35 10 51 


-I-I9-2 


8 Cassiopeiae 


2-8 


20 22'4 


3-86 


N. 59 4 8 16 


4-18-8 


a Ursae Minoris . . (Polaris) 


2"! 


30 13-2 


28-99 


N. 88 51 44 


4-I8-5 


a Eridani .. .. (Achernar) 


06 


34 37'5 


2-23 


s - 57 39 29 


-18-4 


ft Arietis . . ... 


2'7 


50 3-1 


f-3'30 


N. 20 24 10 


+ I7-8 


7 1 Andromedae .. (Almach) 




58 47-8 


3-67 


N - 4 1 55 55 


4-I7-4 


a Arietis . . . . (Hamel) 


2'2 


2 2 29-4 


3-36 


N. 23 4 14 


+ I7-3 


a Ceti . . . . (Menkar) 


2-8 


2 57 56-3 


3-13 


N - 3 45 53 


+ I 4'3 


a Persei .. .. (Mirfak) 


19 


3 18 23-3 


4-27 


N. 49 34 o 


4-13-0 


a Tauri .. .. (Aldebaran) 


1*1 


4 3i 9'4 


+ 3'44 


N. 16 20 36 


+ 7'6 


ft Orionis .. .. (Rigel) 


'3 


5 'o 32-9 


2-88 


S. 8 17 48 


- 4'3 


a Aurigae . . . . (Capella) 


0'2 


5 10 33'3 


4-42 


N. 45 54 54 


+ 4'3 


y Orionis .. .. (Bellatrix) 


'7 


5 20 40-7 


3'22 


N. 6 16 31 


+ 3'4 


ft Tauri .. .. (Nath) 


1-8 


5 21 2'6 


3'79 


N. 28 32 18 


+ 3'4 


a Leporis 


2-7 


5 29 4' 1 


+ 265 


S. 17 52 51 


- 2-7 


e Orionis .. .. (Alnilam) 




5 32 o-i 


3-04 


S. i 15 15 


- 2-4 


Orionis .. . . (1st *) 


2'0 


5 36 34'2 


3-03 


S. i 59 9 


2'0 


a Columbac .. .. (Phact) 


2 '7 


5 36 38 5 


2-17 


S- 34 7 4 


2'O 


K Orionis . . . . (Saiph) 


22 


*) 43 49'2 


2-84 


S. 9 4I 54 


- i'4 


a Orionis . . . . (Betelguese) 


Var. 


5 50 4'7 


+ 3-25 


N- 7 23 33 


4- 0-8 


ft Aurigae . . . . (M enkalinan) . . 


21 


5 53 26 4 


4-41 


N. 44 56 25 


-f 0-6 
+ Q- *; 


ft Canis Majoris 


2'O 


6 19 2-7 


2'6 4 


S. 17 54 50 


u D 
+ i'7 


a Argus . . . . (Canopus) 


-09 


6 22 65 




S. 52 39 o 


+ 1-9 


y Geminorum .. (Alhena) 


I'9 


6 32 55-1 


+ 346 


N. 16 28 16 


- 2-9 


a Canis Majoris .. (Strius) 


-1-6 


6 41 29-3 


2'68 


S 16 36 6 




r Argus 


2-8 


6 47 52-6 


i 49 


S. 50 30 56 


4- 4'2 


e Canis Majoris .. (Adara) 


i 6 


6 55 21-8 


2-36 


S. 28 51 30 




8 Canis Majoris 


2'0 


7 5- jo 


2-44 


S. 26 15 39 


+ 5'6 


TT Argus 


2'7 


7 14 12 6 


4-2-J2 


S. 36 56 52 


4- 6-4 


17 Canis Majoris 


2 '4 


7 20 48-8 


2'37 


S. 29 8 26 


4- 6-9 


a- Geminorum . . (Castor) 


2'0 


7 29 18-3 


3-85 


N. 32 4 19 


7-6 


a Canis Minoris . . (Procyon) 


"5 


7 34 57'4 


3^9 


N. 5 26 19 


- 8-1 


ft Geminorum . . (Pollux) 


J 2 


7 40 M'4 




N. 28 13 40 


- 8-5 


Argus 


23 


8 o 40-0 


4-2'TI 


S. 39 46 8 


4-10-1 


7 Argus 


22 


8 6 58-4 


1-85 


S. 47 5 29 


4- 10*5 


e Argus 


1 7 


8 20 48-7 


l-2 4 


S. 59 14 31 


4-11-6 


5 Argus 


20 


8 42 24-7 


1-66 


S. 54 24 15 


4-13-0 


ft Argus 


1-8 


9 12 17-7 


0-70 


S. 69 22 31 


4-14-9 


i Argus .. .. (Tunis) 


2-3 


9 14 52-o 


+ 1-61 


S. 58 55 36 


4-I5-I 


K Argus 


2-6 


9 19 32-5 


1-86 


S. 54 39 21 


+ I5-3 


a Hydras .. .. (Alphard) 


2'2 


9 23 30-6 


2'95 


S 8 17 54 


+ i5'5 


a Leonis . . . . (Regulus) 


i'3 


10 3 57-2 


3-21 


N. 12 22 24 


17'5 


7 1 Leonis .. .. (Algeiba) 


2-6 


10 15 23-9 


3-29 


N. 20 15 43 


-18-0 


fj. Argus . . . . . . . j 


2-8 


10 43 11-7 


+ 2-57 


S. 48 58 53 


4-18-9 


ft Ursas Majoris . . . . ... 


2-4 


10 56 50*6 


3-63 


N. 56 49 39 


J 9'3 


a Ursae Majoris . . (Dubhe) 
d Leonis . . . . (Zosma) 


2'0 

2-6 


10 58 37-1 
n 9 41-8 


3'74 
3-18 


N. 62 ii 58 
N. 20 58 43 


19-6 


ft Leonis . . . . (Denebola) 


2'2 


it 44 49-6 


3-10 


N. 15 2 10 


2O"O 



8 

THE MEAN PLACES OF 1O8 OF THE BRIGHTEST STARS continued. 



Star's Name. 


Mag. 


Right 
Ascension. 


Annual 
Change. 


Declination- 


Annual 1 
Change. I 


7 Ursse Majoris . . (Phecda) 


2'5 


H. M. S. 
ii 49 28-3 


S. 
4-3'lS 


' o / n 
N. 54 9 22 


n 
20'0 


5 Centauri . . 


2-g 


12 4 3-0 


3-10 


S- 50 15 37 


+ 20'0 


7 Corvi 


2-8 


12 II 32T 


3-09 


S. 17 4 52 


+ 20-0 


a Crucis (mean) 


IT 


12 21 58-6 


3-32 


S. 62 38 23 


+ 20-0 


7 Crucis . . . . . . 


1-6 


12 26 33-0 


3-3I 


S. 56 38 54 


+ I9-9 


7 Centauri . . 


2-4 


12 36 55'9 


+ 3-3I 


S. 48 30 15 


+ I9-8 


ft Crucis .. .. .. 


1-5 


12 42 517 


3'49 


S. 59 14 7 


+ 197 


e Ursae Majoris . . . . 


**7 


12 50 22 '9 


2-6 3 


N. 56 24 36 


-I9'6 


f i Ursae Majoris 


2-4 


13 20 35'2 


2-41 


N. 55 21 31 


-18-8 


a Virginis . . . . (Spica) 


I'2 


13 20 49-1 


3'i6 


S. 10 43 43 


+ 18-8 


e Centauri , . 


2'6 


13 34 37'i 


+ 379 


S. 53 2 42 


+ 18-4 


il Ursae Majoris . . (Benetnasch) 


1-9 


13 44 16-3 ' 


2-38 


N. 49 43 38 


-18-0 


Centauri .. 


3-1 


13 50 21-2 


373 


S. 46 52 49 


4-17-8 


ft Centauri .. 


0-9 


13 57 57'2 


4-21 


S. 59 58 24 


.+ I7'4 


6 Centauri 


2-3 


J 4 i 47'5 


3-56 


S. 35 57 44 


+ I7-3 


a Bootis .. .. (Arcturus) 


O'2 


14 ii 52-5 


4-2-81 


N. 19 36 50 


-16-8 


T] Centauri . . 


2'7 


14 30 13-8 


3'8o 


S. 41 47 38 


+ I5-9 


a 2 Centauri .. 


0'3 


14 33 577 


4'54 


S. 60 29 31 


+ 157 


a Lupi 


2'9 


14 36 24-0 


3-98 


S. 47 i 58 


+ 15-6 


e 2 Bootis .. . . 


2'7 


14 41 21-7 


2-62 


N. 27 25 25 


~ T 5'3 


ft Ursae Minoris . . (Kochab) 


2'2 


14 50 56-0 


O'2O 


N. 74 29 41 


-147 


ft Lupi 


2-8 


14 53 5'3 


+ 3'92 


S. 42 48 2 


+ 14-6 


a Coronae . . . . (Alphacca) 


2- 3 


15 3i io'4 


2'53 


N. 26 59 36 


I2T 


a. Serpentis . . . . (Unukalhai) 


2-8 


15 40 10-7 


2-94 


N. 6 41 9 


-n'5 


8 Scorpii . . 


2'5 


15 55 25-3 


3'54 


S. 22 23 12 


+ 10-4 


p 1 Scorpii .. .. (Akrab) 


2- 9 


16 o 36-5 


+ 3-48 


S. 19 34 45 


+ IO'O 


a Scorpii . . . . (A ntares) 


I'2 


16 24 18-9 


3-67 


S. 26 14 56 


+ 8-1 


f Ophiuchi .. 


2'7 


16 32 35-2 


3-30 


S. 10 24 o 


+ 7'5 


a Trianguli Australis . . 


I'9 


16 39 51-8 


6-32 


S. 68 52 37 


4- 6-9 


e Scorpii 


2'4 


16 44 47-0 


3'93 


S. 34 8 37 


+ 6-5 


77 Ophiuchi 


2-6 


17 5 37' 


+ 3'44 


S. 15 37 24 


+ 47 


ft Arae 


2-8 


17 18 23-8 


4-98 


S. 55 27 10 


+ 3'6 


X Scorpii . . . . . . 


1-7 


17 27 58-2 


4-07 


S. 37 2 40 


+ 2-8 


a Ophiuchi .. .. (Ras Alhague) .. 


2T 


17 3i 4'9 


2-78 


N. 12 37 10 


- 2-5 


6 Scorpii 


2'O 


17 31 2IT 


4'3i 


S. 42 56 47 


+ 2-5 


K Scorpii 


2'5 


17 36 447 


+ 4-15 


S. 38 59 17 


+ 2-0 


7 Draconis . . . . (Rastaban) 


2'4 


17 54 47 


i'39 


N. 51 29 53 


- 0-5 


e Sagittarii .. .. (Kaus Australis) 


2'0 


18 18 39-8 


3'99 


S. 34 25 30 


- 1-6 


a Lyras . . . . ( Vega) 


OT 


18 34 7'7 


2'01 


N. 38 42 21 


+ 3'o 


a Sagittarii . , . . . . 


2T 


18 50 7-2 


372 


S. 26 24 3 


- 4'3 


Sagittarii 


2'7 


18 57 19-9 


+ 3-82 


S. 30 o o 


5'o 


o- Octantis . . .'. 'South Pole Star) 


5'5 


19 27 42-2 


94-42 


S. 89 13 29 


- 7'5 


a Aquilae .. .. (Altair) 


0'9 


19 46 44-0 


2-89 


N. 8 38 54 


+ 9'o 


a Pavonis 


2T 


20 19 5-4 


476 


S. 57 o 7 


-11-4 


7 Cygni 


2- 3 


20 19 14-9 


2T5 


N. 39 59 25 


+ 11-4 


a Cygni . . . . (Deneb) 


I'3 


20 38 36T 


+ 2-04 


N. 44 58 59 


+ 12-8 


e Cygni .. ..- 


2-6 


20 42 5IT 


2-40 


N. 33 39 3i 


+ 13-1 


a Cephei .. .. (Alderamin) 


2-6 


21 16 36-0 


I-4I 


N. 62 14 i 


+ 15-2 


e Pegasi 


2-5 


21 40 6'6 


2-94 


N. 9 29 38 


+ 16-4 


a Gruis 


2*2 


22 3 0'5 


378 


S. 47 21 49 


-I7-5 


ft Gruis 


2'2 


22 37 43-0 


+ 3-58 


S. 47 19 9 


-18-8 


a Piscis Australis . . (Fomalhaut) 


1*3 


22 53 4-0 


3'3Q 


S. 30 3 45 


-19-2 


a Pegasi . . . . (Markab) . . i 2-6 


23 o 37'5 


2-98 


N. 14 45 30 


+ i9'4 



[NOTE. In this table + means add, and - means subtract.] 

In the column headed "Mag." the adopted unit of brightness is designated i -o. The 
magnitudes of stars are deterruined to tenths of a magnitude with reference to this adopted 
unit: thus the value i'6 for Sirius indicates that that star is 2*6 magnitudes brighter than the 
unit ; the value 0-3 for Arcturus indicates that that star is seven-tenths of a magnitude brighter than 
the unit. 



Approximate Apparent Times of the Meridian Passages of the Principal Fixed Stars at 
Greenwich on the First Day of each Month, 1910, 





Name. 


Mag 


Jan. 


Feb. 


Mar. 


April 


May. 


June 


July. 


Aug. 


Sept 


Oct. 


Nov 


Dec. 


ts 
ts 


o Centauri 
a Andromedae 
3 Cassiopeiae . 
a 1 Crucis 
a Phcenicis 


i'8 
2' 

2 4 

2 '4 


H M 

5 ii 
5 i* 
5 i< 
5 3< 
5 3^ 


H. M 

3 < 
3 e 

3 7 

3 24 
3 24 


> i> 
i; 
ii 
3^ 
3! 


H M 

'23 2C 
'2 3 2C 
23 21 

23 3* 

23 JJfc 


H. M 
21 2C 
21 2C 
21 3C 

21 4/ 
2i 4; 


H M 

) 19 2; 
H9 2 : 
> 19 2^; 
'19 4< 
< 9 4! 


H M 
' 17 2; 

r 17 2; 

M7 4< 
i 17 41 


. H. M 
J 15 I* 
JI5 I* 

H5 ic 
>I5 3^ 


H. M H. M 
13 2211 3 . 
13 2311 3, 

*3 2311 3^ 
13 4o|n 52 
13 41 ii 5: 


. H. M 

> 9 3 
\. 9 3? 
5 9 4 < 

9 s: 
; 9 5: 


. H. M. 

> 7 36 
) 7 36 

> 7 36 
' 7 53 
' 7 54 


ts 

ts 


7 Crucis 
7 Centauri 


I 6 

2 , 


5 4J 
5 5 1 


3 25 
3 35 


4 C 
5c 


23 43 
23 53 


21 5] 
22 1 


19 4? 
J 9 5S 


H7 45|'5 41 
H7 55;i5 51 


13 45 
13 55 


I T 5' 
12 5 


IO 1 
10 15 


7 58 

8 8 


ts 

tN 


/3 Ceti 
3 Crucis 
r c Ursae Majoris 


22 


5 54 
5 55 
6 4 


3 4i 
3 45 
3 52 


52 
56 
2 3 


23 55 

O 1 

o re 


22 4 
22 I 

22 I< 


20 2 
20 
20 I.; 


17 5* 
, 18 i 
[18 c 


'i'5 53 
*5 57 
) 16 4 


'3 5* 
14 i 

M f J 


12 1C 
12 13 
12 21 


IO It 

10 i 

10 2< 


8 Tl 

8 14 

8 22 


j 7 Cassiopeiae . . 


2'3 


6 f 


3 54 


2 c 


O II 


22 1C 


20 I/] 


18 ic 


16 e 


14 ic 


I 2 21 


IO '2t 


8 23 


tN 


' 3 Andromedae . . 
5 Cassiopeiae . . 
f ! Ursae Majoris 
Polaris 


2 < 

2 

21 


6 ic 
634 

6 35 

6 4 i 


4 7 
4 22 
4 23 
4 29 


2 I* 

2 33 

2 34 
2 35 


o 25 
o 40 
o 40 
o 46 


22 3 C 

22 4 = 

22 4 e 

22 5 I 


20 2} 

20 43 
20 42 
20 45 


18 2; 

18 3c 

i83S 
18 45 


16 ic 
16 34 
16 35 
16 41 


M 2. 

M 35 
14 35 
14 4 C 


12 3 e 

12 51 
12 5-1 

12 55 


10 4C 
10 5f 
io 5: 

" 3 


8 36 
8 52 
852 
8 59 


ts 

tN 


e Centauri 
Achernar 
t\ Ursae Majoris 


26 


6 48 
6 49 
6 58 


4 36 
4 37 
4 46 


2 47 

2 48 
2 56 


o 54 
54 


22 59 
22 59 
23 9 


20 57 
20 57 
21 7 


18 53 

18 53 
19 3 


16 48 
16 49 
16 58 


14 53 
14 51 
15 3 


13 5 

13 15 


i 9 
1 9 
i 19 


9 6 
9 6 
9 T 6 


Arietis 
fSha Centauri 


2'7 
08 


7 4 
7 12 


4 52 
5 o 


3 3 
3 ii 


9 
17 


23 15 
23 23 


21 12 
21 20 


19 8 
19 16 


17 4 
17 J2 


15 

15 16 


13 20 
13 28 


i 25 
i 32 


9 21 
9 29 


ts 
ts 


7 l Andromedae . . 
Centaun 
o Arietis 
a 4 Centauri 


2'2 

21 
22 
TO 


7 13! 5 i 
7 18 5 4 
7 16 5 4 
7 48 5 35 


3 12 
3 15 
3 '5 
3 47 


18 

21 
22 

53 


23 23 
23 26 
23 27 

2 


21 21 
21 2 4 
21 25 
21 56 


19 17 

19 20 
19 21 
19 52 


7 13 
17 16 

17 17 
i? 48 


15 17 

15 20 
15 21 

15 52 


13 29 
13 32 

13 33 
14 4 


ii 33 
it 36 
ii 37 
12 9 


9 30 
9 33 
9 34 
10 5 


tS i a Lupi 


2'5 


7 50 


5 38 


3 49 


56 


o 5 


21 58 


19 54 


17 50 


15 54 


T 4 7 


12 II 


10 7 


IN 


)8 Ursae Minoris 


22 


8 5 


5 53 


4 4 


2 II 


o 20 


22 13 


20 9 


18 5 


16 9 


14 21 


12 26 


IO 22 




o Ceti 


2-8 


8 12 


6 o 


4 


2 17 


o 26 


22 2O 


20 1 6 


18 12 


16 16 


I 4 28 


12 32 


10 29 


a Persei 

j A Ideba-ran 


19 

T.-I 


8 32 6 20 
9 44 7 32 


4 3 1 
5 44 


2 37 
3 50 


o 47 
i .59 


22 40 
23 53 


20 36 

21 49 


18 32 
19 44 


16 36 
J 7 49 


1448 
16 I 


12 53 
14 5 


io 49 

12 2 


tS j a Tri. Australis 


19 


9 53 


7 4 1 


5 52 


3 59 


2 8 


5 


21 57 


19 53 


17 57 


16 9 


14 14 


12 10 


Capella 


02 


10 24 


8 12 6 23 


4 29 


2 3$ 


o 36 


22 28 


20 24 


18 28 


6 40 


14 44 


12 41 


Rigel 


o'3 


10 24 


8 12 6 23 


4 30 


2 39 


o 36 


22 28 


20 24 


18 28 


6 40 


J 4 45 


12 41 


tS & Arae 


2-7 


10 31 


8 19! 6 30 


4 37 


2 4 6 


o 44 


22 36 


2O 31 


18 36 


6 48 


14 52 


12 49 


7 Orionis .. 1-7 


10 34 


8 22 6 33 


4 40 


2 49 


o 46 


22 3 8 


20 34 


1 8 38 


16 50 


14 55 


12 51 




3 Taun - .. 


1-8 


10 34 


8 22 


6 33 


4 40 


2 49 


o 47 


22 39 


20 34 


1 8 39 


16 51 


14 55 


12 52 




o Leporis 


27 


10 42 


8 30 


6 41 


448 


2 57 


o 55 


22 47 


20 42 


1847 


16 59 


15 3 


13 




e Orionis 


17 


10 45 


8 33 


6 44 


4 5i 


3 o 


o 58 


22 50 


20 46 


18 50 


17 2 


15 6 


13 3 




Orionis 


2'0 


TO 5O 


8 38 


6 49 


4 55 


3 4 




22 54 


20 51 


18 54 


17 6 


15 II 


13 7 




<c Orionis 


2'2 


10 57 


845 


6 56 


5 3 


3 12 


9 


23 I 


20 57 


19 i 


7 M 


15 18 


3 14 




Betelguese 


Var. 


ii 4 


8 52 


7 3 


5 9 


3 19 


16 


23 8 


21 4 


19 8 


7 20 


15 25 


13 21 




Aurigae 


2'I 


i 6 


8 54 


7 6 


5 12 


3 21 


19 


23 ii 


21 6 


19 ii 


17 23 


15 27 


13 24 




Aurigae 


2-7 


7 


8 55 


7 6 


5 13 


3 22 


20 


23 ii 


21 7 


19 ii 


17 24 


15 28 


13 25 


tN 


7 Draconis 


2'4 


i 8 


8 56 


7 7 


5 14 


3 23 


20 


23 12 


21 8 


19 12 


17 25 


15 29 


J 3 25 




j8 Canis Majoris 


2'O 


i 32 


9 20 


7 3 1 


5 38 


3 47 


45 


23 37 


21 3 2 


19 37 


17 49 


15 53 


13 50 




Canopus 


--I'D 


i 35 


9 23 


7 34 


5 41 


3 50 


48 


23 40 


21 35 


19 40 


17 52 


15 56 


13 53 




7 Geminorum . 


I'9 


46 


9 34 


7 45 


5 52 


4 i 


I 58 


23 50 


21 46 


19 50 


18 3 


16 7 


14 3 


tN 


FVgw 


O'l 


47 


9 35 


7 46j 5 53 


4 2 


2 


23 52 


21 47 


19 52 


18 4 


16 8 


M 5 




Sirius 


1*4 


55 


9 43 7 54J 6 o 


4 9 


2 7 


o 3 


21 55 


19 59 


18 ii 


16 15 


14 12 




T Argus 


2-8 


2 I 


9 49! 8 o 


6 7 


4 16 


2 13 


O 10 


22 I 


20 5 


18 18 


l6 22 


14 18 




c Canis Majoris 


1-6 


2 8 


9 56| 8 8 


6 14 


4 23 


2 21 


o 17 


22 8 


20 11 


18 2.5 


16 29 


14 26 




5 Canis Majoris 


2'O 


2 l8 


co 6 


8 17 


6 24 


4 33 


2 30 


o 27 


22 18 


JO 22 


[8 35 


16 39 


4 35 




TT Argus 


2 7 


2 27 


co 15 


8 26 


6 33 


4 42 


2 40 


o 36 


22 27 


jo 32 


c8 44 


6 48 


H 45 




77 Canis Majoris 


2 '4 


2 34 


CO 22 


8 33 


6 40 


4 49 


2 46 


o 42 


22 34 


JO 38 


18 50 


c6 55 


[4 51 




Castor 


2'0 


2 42 


co 30 


8 41 


6 48 


4 57 


2 55 


o 51 


Z2 42 


>O 46 


18 59 


E/ 3 


^5 o 




Procyon 


0'5 


2 48 


co 36 


847 


6 54 


5 3 


3 o 


o 56122 48 


:o 52 


9 4 


7 9 


5 5 




Pollux 


I'2 


2 53 


co 41 


8 52 


6 59 


5 8 


3 5 


2 22 53 


'o 57 


9 10 


7 M 


[5 1 




f Argus 


2'3 


3 J 4 


[I 1 


9 13 


7 19 


5 28 


3 26 


22 2 3 14 


!I 18 


9 30 


7 34 


5 3i 




7 Argus 


1*9 


3 20 ] 


LI 8 


9 19 


7 26 


5 35 


3 32 


28 23 20 


>I 24 


9 37 


7 4 1 


5 37 


ts 


a Pavonis 


2'O 


3 3 2 i 


I 20 


9 3 1 


7 38 5 46 


3 44 


40 23 32 


>I 36 


9 48 


7 52 


5 49 




e Argus 


17 


3 34 ^ 


[I 23 


9 33 


7 * 5 49 


3 46 


42. 


23 34 


51 38 


9 50 


7 55 


5 5 T 



t N. or tS. These times relate to the Meridian Passages of Circumpolar Stars at the Inferior Transit, 
N. or S. denoting the Declination of the Star. 



10 

Approximate Apparent Times of the Meridian Passages of the Principal Fixed Stars at 
Greenwich on the First Day of each Month, 1910 continued. 





Name. 


Mag. 


Jan. 


Feb. 


Mar. 


April. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 








H. M 


H. M 


H. M. 


H. M. 


H. M 


H. M 


H. M. H. M. 


H. M. 


H. M. 


H. M. H. M. 


IN 


a Cygni 


i'3 


13 sijii 40 


9 50 


7 57 


6 6 


4 4 


2 


23 51 


21 56 


20 8 


18 12 


16 9 




5 Argus .. 20 


'3 55" 43 


9 54 


8 i 


6 10 


4 8 


2 4 


23 55 22 o 


2O 12 


18 16 


16 13 




B Argus .. 1-7 


14 2512 13 


10 24 


8 31 


6 40 


4 38 


2 34 


29 22 30 


20 42 


18 46 


16 42 




i Argus 


2-2 


14 2812 16 


ro 27 


8 33 


6 42 


4 40 


2 3 6 


32J22 32 


20 44 


18 49 


16 45 


<N 


a Cephei 


2-6 


14 29JI2 17 


10 28 


835 


644 


4 42 


2 3 8 


o 33 


22 34 


20 46 


18 50 


16 47 




ic Argus 


2-6 


14 32JI2 20 


10 31 


8 38 


6 47 


4 45 


2 41 


o 36 


22 37 


20 49 


18 53 


16 50 




a Hydras 


2'2 


14 3612 24 


10 35 


842 


6 5i 


4 49 


2 45 


O 40 22 40 


20 53 


18 57 


16 53 


ts 


a Gruis 


19 


15 1513 3 


ii 14 


9 21 


7 30 


5 28 


3 24 


19 


23 20 


21 32 


19 36 


J 7 33 




Regulas 


I'3 


15 16113 4 


ii 16 


9 22 


7 3i 


5 29 


3 25 


20 


23 21 


21 33 


19 37 


17 34 




7 1 Leonis 


"5 


15 28JI3 16 


ii 27 


9 34 


7 43 


5 40 


3 36 


32 


23 32 


21 44 


19 49 


17 45 


ts 


B Gruis 


2-1 


15 50 


13 38 


ii 49 


9 56 


8 5 


6 2 


3 59 


54 


23 55 


22 7 


20 n|i8 7 




p. Argus 


2-8 


15 55 


13 44 


ii 55 


IO I 


8 10 


6 8 


4 4 


59 


o 4 


22 12 


10 16 


18 13 




B Ursae Majoris 


2- 4 


16 9 '3 57 


12 8 


10 15 


8 24 


6 22 


4 18 


2 13 


o 17 


22 26 


20 30 


18 26 


Dubhe . . 2 - o 


16 ii 


13 59 


12 IO 


10 17 


8 26 


6 23 4 19 


2 IS 


o 19 


22 28 20 32 


18 28 




5 Leonis 


2'6 


16 22 


14 10 


12 21 


10 28 


8 37 


6 34 


4 30 


2 26 


o 30 


22 39J20 43 |i8 39 




B Leonis 


2'2 


16 57 


M 45 


12 56 


" 3 


9 12 


7 9 


5 6 


3 i 


5 


23 1421 1819 14 


7 Ursae Majoris 


2'5 


17 i 


M 50 


13 * 


ii 7 


9 16 


7 M 


5 10 


3 6 


10 


23 l8|2I 22 19 19 


5 Centauri 


2-8 


17 16 


15 4 


13 15 


II 22 


9 3i 


7 29 


5 25 


3 20 


24 


23 3321 3719 33 


fN \B Cassiopeiae .. 


2- 4 


17 17 


15 5 


13 16 


II 2 3 


9 32 


7 29 


5 25 


3 21 


25 


23 3421 38'i9 34 




7 Corvi 


2-7 


i? 23 


15 12 


*3 23 


II 2Q 


9 ^8 


7 36| 5 32 


3 28 


3223 40 


21 44 19 41 




a 1 Crucis 


I'O 


17 34 


15 22 


13 3311 40 9 49 | 7 4 6| 5 43 


3 3 


42 


23 5i 


21 55 


19 5i 


ts 


a Phoenicis 


2-4 


17 34 


15 22 


13 3311 40 


9 49! 7 47i 5 43 


3 38 


42 


23 5i 


21 55 


19 52 




7 Crucis 


1-6 


17 38 


15 27 


13 SSjii 44 


9 53 7 5i 


5 47 3 43 


1 4723 55 


21 59 


19 56 




7 Centauri 


2-4 


17 49 


15 37 


13 48 ii 55 10 48 i 


5 57j 3 53 


i 57 


o 9 


22 IO 


20 6 




B Crucis 


i'5 


17 55 


15 43 


13 54JI2 i 


10 IO 


8 7 


6 3 


3 59 


2 3 


o 15 


22 16 


20 12 




e Ursae Majoris 


1-8 


18 2 


15 50 


14 2 


12 8 


10 17 


8 15 


6 ii 


4 6 


2 IT 


o 23 


22 2 3 


20 19 


fN 7 Cassiopeise . . 


2-3 


18 3 


15 52 


14 3 


12 9 


10 18! 8 16 


6 12 4 8 


2 12 


o 24 


22 2 4 


2O 21 


JN \B Andromedae . . 


2-4 


18 17 


16 5 


14 16 


12 23 10 32 8 29 


6 25 


4 21 


2 25 


o 37 


22 3 8 


20 34 


fN 


5 Cassiopeiae . . 


2-8 


18 32 


16 20 


14 31 12 38110 47 


845 


6 41 


4 36 


2 40 


o 53 


22 53 


20 49 




f 1 Ursse Majoris 


21 


18 32 


16 2i|i4 32 12 3|ro 47 


8 45 6 41] 4 37 


2 4 I 


o 53 


22 53 


20 50 




Spica 


ra 


18 33 16 21 


M 32 


12 3910 48 


8 45! 6 41 


4 37 


2 4 1 


o 53 


22 53 


20 50 


fN 


Polaris 


21 


18 3916 27 


14 37 


12 4410 53 


8 51 


6 47 


4 43 


2 48 





23 I 


20 57 


ts 


Achernar 


0'5 


18 46 16 35 14 46 


12 52 II I 


8 59 


6 55 


4 5i 


2 55 


7 


23 7 


21 4 




e Centauri 


26 


18 46 16 34 14 46 


12 52 II I 


8 59 


6 55 


4 50 


2 55 


7 


2 3 7 


21 4 




97 Ursaa Majoris 


19 


18 56 


16 44 


14 55 


I 3 2 


ii ii 


9 9 


7 5 


5 o 


3 4 


<7 


23 17 


21 13 




i" Centauri 


2-8 


19 2 


16 50 


15 i 


13 8 


ii 17 


9 15 


7 ii 


5 6 


2 10 


22 


23 23 


21 19 




B Centauri 


0-8 


19 916 5815 9 


13 15 


ii 24 


9 22 


7 18 


5 -M 


3 18 


3 


23 3 


21 27 


]N 


7 1 Andromedae . 


2'2 


19 10 16 58 


15 1013 1611 25 


9 23 


7 19 5 14 


3 19 


31 


23 3i 


21 28 




6 Centauri 


2'1 


19 1317 '2 


15 i3'3 19 


ii 28 


9 26 


7 22 


5 17 


3 22 


34 


23 34 


21 31 




Arcturus 


0-3 


19 2317 12 


15 2313 30 


ii 39 


9 36 


7 32 


5 28 


3 32 


44 


23 44 


21 4 I 


f\ Centauri 


2'7 


19 42 


17 30 


15 4* 


13 48 


ii 57| 9 54 7 50 


5 46 


3 50i 2 2 


o 721 59 


i a 2 Centauri 


I O 


19 45 


17 34 


15 45 


13 5i 


12 o 9 58 


7 54 


5 5" 


3 54J 2 6 


O IO 


22 3 


a Lupi 


2-5 


19 48 


17 36 


*5 47 


13 5412 3|io o 


7 56 


5 52 


3 56 


2 8 


o 13 


22 5 


e 2 Booris 


26 


19 53 


17 41 


15 5213 5912 810 6 


8 2 


5 57 


4 i 


2 13 


o 18 


22 IO 




B Ursae Minori.s 


2 2 


20 3 


17 5i 


16 2 


'4 9 


12 l8 


10 15 


8 12 


6 7 


4 ii 


2 2 3 


o 28 


22 2O 




B Lupi 


2'7 


2O 4 


17 53 


16 4 


74 ic 


12 19 


10 17 


8 13 


6 9 


4 13 


2 25 


o 29 


22 22 


tM 


a Persei 


19 


2O 30 


18 18 


16 29^4 36 12 45 10 42 


8 3 S 


6 34 


4 38 


2 50 


o 55 


22 47 




Aiphacca 


23 


20 43 


1 8 31 


16 42 


14 4912 5810 55 


8 57 


6 47 


4 5i 


3 3 


i 7 


23 o 




a Serpentis 


2-8 


20 51 


1 8 40 


16 51 


M 5^3 7 


ii 4 9 o 


6 56 


5 o 


3 12 


i 16 23 9 




5 Scorpii 


2-5 


21 7 


18 55 


17 6 


15 1313 22 


ii igj 9 15 


7 ii 


5 15 


3 27 


i 32 


23 2 4 




/3 1 Scorpii 


2-7 


21 I2ig 


17 n 


15 18 


13 2 7 


II 24 


9 21 


7 16 


5 20 


3 32 


i 37 


23 29 




Antares 


i'3 


21 35 


19 24 


17 35 


15 42 


13 5<; 


II 48 


9 44 


7 4 


5 44 


3 56 


2 


23 53 




Ophiuchi 


2-7 


21 44 


19 32 


!7 43 


15 50 


13 59 


11 56 


9 52 


748 


5 52 


4 4 


2 9 


o 5 




a Tri. Australis 


l-Q 


21 51 


19 39 


17 50 


15 57 


14 6 


12 3 


9 59 


7 55 


5 59 


4 ii 


2 16 


12 




e Scorpii . 2' 3 


21 5 6 


19 44 


'7 55 


16 2 


14 ii 


12 8 


10 5 


8 o 


6 4 


4 16 


2 21 


o 18 




17 Ophiuchi 


2-6 


22 17 


20 5 


18 16 


16 23 


14 32 


12 29 


10 25 


8 21 


6 25 


4 37 


2 42 


o 38 


t-R 


Capella 


O"2 


22 21 


20 10 


18 21 


16 28 


H 36 


T 2 34 


10 30 


8 26 


6 30 


4 42 


2 46 


o 43 




B Aras 


2'7 


22 29 


20 17 


18 29 


16 35 


14 44 


12 42 


10 38 


8 33 


6 38 


4 5o; 2 54 


o 51 




X Scorpii 


1-8 


22 39 


20 27 


18 38 


1 6 45 


J 4 54 


12 52 


10 48 


8 43 


6 47 


5 o; 3 4 


i i 




a Ophiuchi 


2'I 


22 42 


20 30 


18 42 


16 48 


M 57 


12 55 


10 51 


8 46 


6 5i 


533' 


i 4 



j-N. or fS. These times relate to the Meridian Passages of Circumpolar Stars at the Inferior Transit, 
N. or S. denoting the Declination of the Star. 



11 



Approximate Apparent Times of the Meridian Passages of the Principal Fixed Stars at 
Greenwich on the First Day of each Month, \9\Q-contimied. 





Name. Mag. 


Jan. 


Feb. 


Mar 


April. 


May. 


June. July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 




6 Scorpii .. 2~o 


H. M 
22 42 


H . M . 
20 30 


H. M. 

18 42 


H. M. 

16 48 


H. M. 

H 57 


H. M. 

12 55 


H. M. H. M. 

10 511 8 46 


H. M. H. M. 

6 5i 5 3 


H. M. 

3 7 


H. M. 

4 




K Scorpii . . 2 -6 


22 4 8 


20 36 


18 47 


16 54 


J 5 3 


13 o 


10 56: 8 52 


6 56 5 8 


3 13 


9 


fN 


/8 Aurigae . . 2~i 


23 4 


20 52 


19 4 


17 10 


15 19 


13 i7|H 13 9 8 


7 13 


5 25 


3 29 


26 




7 Draconis . . 2-4 


23 6 


20 54 


!9 5 


17 12 


15 21 


13 18 


ii 15 9 10 


7 14 


5 26 


3 3i 


28 




e Sagittani . . 1-9 


23 29 


21 l8 


19 29 


I 7 36 


15 44 


13 42 


ii 38 9 34 


7 38 


5 50 


3 54 


5i 


ts 


Canopus . ., i - o 


23 33 


21 21 


19 33 


r 7 39 


15 48 


13 4 6 


ii 42 


9 37 


7 42 


5 54 


3 58 


i 54 




Vega .. 


O'l 


23 45 


21 33 


19 44 


17 5i 


16 o 


13 58 


ii 54 9 49 


7 53 6 6 


4 10 


2 7 


ts 


r Argus 


2-8 


3 


21 47 


i9 58 


18 5 


16 14 


14 n 


12 710 3 


8 yj 6 20 


4 24 


2 21 




cr Sagittarii 


2'I 


o 5 


21 49 


20 


18 7 


16 16 


H 13 


12 1010 5 


8 9 6 22 


4 26 


2 23 




Sagittarii . . 27 


12 


21 56 


20 7 


18 14 


16 23 


14 21 


12 I7|lO 12 


8 16 6 29 


4 33 


2 30 




Altair. , . . 0-9 


2 


22 4 6 


20 57 


19 3 


17 12 


15 10 


13 6 


II 2 


9 6 


7 18 


5 22 


3 19 


ts 


7 Argus . . 1-9 


22 


23 6 


21 17 


19 24 


17 33 


15 30 


13 26 


II 22 


9 26 


7 38 


5 43 


3 39 




a Pavonis . . 2-0 


33 


23 18 


21 29 


19 36 


17 44 


15 42 


13 38 


II 34 


9 38 


7 50 


5 54 


3 5i 




7 Cygni ..] 2-3 


3423 18 


21 29 


19 36 


17 45 


15 42 


J 3 39|n 34 


9 38 


7 5i 


5 55 


3 52 


ts 


c Argus 


i*7 


36 


23 20 


21 31 


19 3"8 


J 7 47 


15 44 


13 40 


II 36 


9 4 


7 52 


5 56 


3 53 




a Cygni 


i'3 


54 


23 37 


21 49 


19 55 


18 4 


16 2 


13 58 


ii 53 


9 58 


8 10 


6 14 


4 12 


ts 


5 Argus . . 2-0 


57 


23 4i 


21 53 


19 59 


18 8 


16 6 


14 2 


ii 57 


10 I 


8 14 


6 18 


4 15 




c Cygni . . 2-6 


58 


23 42 


21 53 


20 O 


18 8 


16 6 


14 2 


II 58ilO 2 


8 14 


6 18 


4 15 


ts 


Argus 


17 


2 27 


o 15 


22 22 


2O 29 


18 38 


16 36 


14 32 


I22 7 


10 31 


844 


6 48 


4 45 


ts 


i Argus 


2'2 


2 30 


o 18 


22 25 


20 32 


18 40 


1 6 38 


14 34 


12 30 


10 34 


8 46 


6 50 


4 47 




a Cephei 


2-6 


2 31 


o 19 


22 27 


20 33 


18 42 


16 40 


14 30 


12 31 


10 36 


8 48 


6 52 


4 49 


K Argus 


2-6 


2 34 


O 22 


22 30 


20 36 


18 45 


1 6 43 


M 39 


12 34 


10 38 


8 51 


6 55 


4 52 




( Pegasi 


2'5 


2 55 


o 43 


22 50 


20 57 


19 6 


17 3 


14 59 


12 55 


10 59 


9 " 


7 15 


5 12 




a Gruis 


I'9 


3 i? 


i 5 


23 13 


21 19 


19 28 


17 26 


15 22 


13 17 


II 22 


9 34 


7 38 


5 35 




Gruis 


2'I 


3 52 


i 40 


23 47 


21 54 


20 3 


18 o 


15 56 


13 52 


II 56 


10 9 


8 12 


6 10 




Fomalhaut 


I'3 


4 7 


i 55 


o 6 


22 9 


20 18 


18 16 


16 12 


14 7 


12 12 


10 24 


8 28 


6 25 


N j8 Ursae Majoris 


2- 4 


4 ii 


i 59 


O 1022 13 


20 22 


18 19 


16 16 


.14 ii 


12 15 


10 28 


8 32 


6 29 


Ni Dubhe 


2'0 


4 13 


2 I 


O 1222 15 


20 24 


18 21 


16 17 


14 13 


12 17 


10 29 


8 34 


6 30 


a Pegasi 


2-6 


4 15 


2 3 


o 1422 17 


20 26 


18 23 


16 19 


14 15 


12 19 


10 31 


8 36 


6 32 


fNJ 7 Ursae Majoris 


2'5 


5 4 


2 52 


I 3 l2 3 6 


21 15 


19 12 


17 8 


15 4 


13 8 


II 20 


9 24 


7 21 



t N or t S. These times relate to the Meridian Passages of Circumpolar Stars at the Inferior Transit, N. or 
S. denoting the Declination of the Star. 

Correction of the Times in the preceding Table for the Day of the Month (to be subtracted}. 



Days. 


Jan. 


Feb. 


Mar. 


April. 


May. 


June. 


July. 


Aug. 


Sept. 


Oct. 


Nov. 


Dec. 




H M. 


H. M. 


H M. 


H, M. 


H M 


H. M 


H. M. 


H. M. 


H. M. 


H. M. 


H. M. 


H. M. 


I 


O 


O O 

















O 





O 


O 





2 


o 4 


o 4 


o 4 


o 4 


o 4 


o 4 


o 4 


o 4 


o 4 


o 4 


o 4 


o 4 


3 


o 9 


o 8 


o 7 


o 7 


o 8 


o 8 


o 8 


o 8 


o 7 


o 7 


o 8 


o 9 


4 


o 13 


12 


II 


II 


II 


12 


12 


12 


II 


II 


12 


o 13 


5 


o 18 


o 16 


o 15 


o 15 


o 15 


o 16 


o 16 


o 15 


o 14 


o 15 


O 16 


o 17 


6 


22 


20 


o 19 


o 18 


o 19 


21 


21 


o 19 


o 8 


o 18 


O 20 


22 


7 


o 26 


o 24 


22 


22 


o 23 


o 25 


o 25 


o 23 


22 


22 


o 24 


o 26 


8 


o 30 


o 28 


o 26 


o 26 


o 27 


o 29 


o 29 


o 27 


o 25 


o 25 


o 28 


o 30 


9 


o 35 


o 32 


o 30 


o 29 


o 30 


o 33 


o 33 


o 31 


o 29 


o 29 


o 32 


o 35 


10 


o 39 


o 36 


o 33 


o 33 


o 35 


o 37 


o 37 


o 35 


o 32 


o 33 


o 36 


o 39 


ii 


o 43 


o 40 


o 37 


o 36 


o 39 


o 41 


o 41 


o 38 


o 36 


o 37 


o 40 


o 44 


12 


o 48 


o 44 


o 41 


o 40 


o 42 


o 45 


o 45 


o 42 


o 40 


o 40 


o 44 


o 48 


13 


o 52 


o 48 


o 44 


o 44 


o 46 


o 49 


o 49 


o 46 


o 43 


o 44 


o 48 


o 52 


M 


o 56 


o 52 


o 48 


o 48 


o 50 


o 54 


o 53 


o 50 


o 47 


o 48 


o 52 


o 57 


15 


I 


o 56 


o 52 


o 51 


o 54 


o 58 


o 57 


o 53 


o 50 


o 51 


o 56 


i 


16 


5 


o 


o 55 


o 55 


o 58 


2 


i 


o 57 


o 54 


o 55 


o 


6 


17 


9 


3 


o 59 


o 59 


I 2 


6 


5 


i i 


o 58 


o 59 


4 


10 


18 


13 


7 


2 


2 


i 6 


IO 


9 


5 


i i 


3 


9 


15 


19 


18 


ii 


6 


6 


I IO 


14 


13 


8 


i 5 


6 


13 


19 


20 


22 


15 


10 


IO 


I 14 


i 19 


17 


12 


i 8 


10 


17 


24 


21 


26 


19 


14 


13 


i 18 


23 


21 j 


16 


12 


14 


21 


28 


22 


31 


23 


17 


17 


I 22 


27 


25 


19 


16 


18 


25 


32 


23 


35 


26 


21 


21 


I 26 


3i 


29 


23 


19 


21 


30 


37 


2 4 


39 


3 


24 


25 


30 


35 


33 


27 


23 


25 


34 


4i 


25 


43 


34 


28 


28 


34 


39 


37 


3i 


26 


29 


38 


46 


26 


47 


38 


32 


32 


38 


44 


4i 


34 


30 


33 


42 


50 


27 


51 


42 


35 


36 


42 


48 


45 


38 


34 


37 


47 


55 


28 


56 


45 


39 


4 


46 


52 


49 


42 


37 


4i 


5i 


59 


29 


2 




43 


44 


50 


i 56 


53 


45 


i 4i 


44 


55 


2 3 


3 


2 4 




46 


47 


55 


2 


57 


49 


i 44 


48 


59 


2 8 


31 


2 8 




50 




so 





i 


5 2 





5 2 , 




2 12 



12 



Table A. 

When hour angle is less than 5 hours, name the factors taken from Table A contrary to name of lat. 





HOURS. 


IHr. 


3 


m. 


Var. 
tol' 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


M 


01 


of 


4 





12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 






Lat. 




i 


























e 


i 
( 


4-00 


I 

oo 


oo 


oc 


I , 








'00 


i 
oo 



oo 


i 

oo 


oo| 'oo 


/ 
oo 


i 
oo 


oo 


oo 


oo 


oo 




4'c 


4-00 


I'OO 


50 


*33 


'25 


20 


17 


I, 


12 


II 


'10 


09 


08 


08 


07 


07 




8-c 


4-01 


2-00 


I'OO 


67 


-50 


40 


33 


zi 


25 


'22 


'20 


18 


16 


'*5 


* J 4 


13 




I2*C 


4-01 


3 -00 


1-50 


I -00 


"75 


60 


-50 


-43 


'37 


'33 


'3D 


27 


'25 


* 2 ' 


'21 


'20 


t 


i6-c 


4-02 


4 -OI 


2'OO 


1-33 


I'OO 


80 


66 


'57 


'SO 


"44 


40 


36 


'33 


3 


28 


26 




20-1 


4-03 


5-01 


2-51 


1-67 


1-25 


I -00 


83 


71 


62 


'55 


'SO 


'45 


41 


38 


"35 


"33 


6 


24- 


4-05 


6-02 


3-01 


2-01 


1-50 


I '20 


I'OO 


86 


75 


66 


60 


'54 


'49 


46 


42 


'39 




28-1 


4-06 


7-03 


3-52 


2-34 


1-76 


I- 4 


1-17 


I'OO 


87 


78 


70 


63 


58 


'53 


'49 


4 6 




32-2 


4-08 


8-05 


4-02 


2-68 


2"OI 


1-61 


i '34 


1-14 


I'OO 


89 


80 


72 


66 


61 


56 


52 


g 


36-2 


4-10 


9-07 


4'54 


3-02 


2-27 


1-81 


i'5i 


1-29 


1-13 


I'OO 


90 


81 


'75 


69 


64 


"59 


IO 


40-4 


4-12 


lO'I 


5-05 


3-36 


2-52 


2-02 


1-68 


1-44 


i '25 


i*ii 


I'OO 


91 


83 


76 


71 


66 


II 


44*5 


4-15 


in 


5-57 


37 1 


2-78 


2'22 


1-85 


1-58 


r 3 8 


1-23 


no 


I'OO 


91 


84 


78 


73 


12 


48-7 


4-18 


12*2 


6-09 


4-06 


3-04 


2'43 


2'O2 


173 


1-51 


i-34 


I'2I 


1*09 


I'OO 


92 


85 


79 


13 


52-g 


4-21 


13-2 


6-61 


4-41 


3-30 


2-64 


2'2O 


r88 


1-64 


1-46 


1-31 


1*19 


1-09 


I'OO 


'93 


86 


!<: 


57' 1 


4-25 


14-3 


7-14 


4-76 


3'57 


2-85 


2-37 


2-03 


177 


i'57 


1-41 


1-28 


1-17 


I -08 


I -00 


'93 


15 


61-4 


4-29 


J 5'4 


7-67 


5'" 


3-83 


3-06 


2-55 


2'l8 


1-91 


1-69 


1-52 


1-38 


1-26 


1-16 


1-07 


I '00 


16 


657 


4-33 


16-4 


8-21 


5-47 


4 -IO 


3-28 


273 


2-34 


2-04 


r8i 


1-63 


1-48 


i'35 


1-24 


I-I5 


1-07 


17 


70-1 


4-37 


i7'5 


8-75 


5-83 


4'37 


3'49 


2-9I 


2-49 


2-18 


i-93 


173 


i '57 


1-44 


1-32 


1-23 


1-14 


18 


74*5 


4-42 


18-6 


9*30 


6-20 


4^5 


37i 


3-09 


2-65 


2-31 


2-05 


1-84 


1-67 


i'53 


1-41 


1-30 


I'2I 


19 


78-9 


4-47 


197 


9-86 


6-57 


4-92 


3-94 


3-28 


2 '8o 


2-45 


2-17 


i-95 


177 


1-62 


1-49 


1-38 


1-29 


20 


83-4 


4-53 


20-9 


10-4 


6 - 9/ 


5'2I 


4-16 


3H6 


2-96 


2-59 


2-30 


2-06 


1-87 


171 


1-58 


r6 


1-36 


21 


88-0 


4-59 


22-0 


II'O 


7'32 


5-49 


4-39 


3^5 


3' J 3 


2-73 


2-42 


2-18 


1-97 


1-81 


1-66 


i'54 


i '43 


22 


92-6 


4-65 


23-I 


n-6 


771 


578 


4-62 


3-84 


3-29 


2-87 


2'55 


2-29 


2-08 


1-90 


i'75 


1-62 


i'5i 


23 


97'3 


4-72 


24-3 


I2'2 


8-10 


6-07 


4-85 


4-04 


3H6 


3-02 


2-68 


2-41 


2-18 


2'OO 


1-84 


170 


1-58 


2/ 


IO2'O 


4-79 


25-5 


I2'7 


8-50 


6-37 


5-09 


4-24 


3-63 


3-17 


2'8l 


2-53 


2-29 


2*09 


i'93 


179 


1-66 


25 


1 06 -9 


4-87 


267 


I3H 


8-90 


6-67 


5-33 


4'44 


3-80 


3-32 


2-94 


2-64 


2-40 


2-I9 


2 -O2 


1-87 


174 


26 


ixi-8 


4-95 


27-9 


14-0 


9-3i 


6-97 


5-57 


4-64 


3-97 


3'47 


3-o8 


277 


2-51 


2-29 


2'II 


1-96 


1-82 


27 


116-8 


5-04 


29-2 


I 4 -6 


9'72 


7-29 


5-82 


4-85 


4-15 


3-63 


3'22 


2-89 


2-62 


2-40 


2'2I 


2-04 


1-90 


28 


121-9 


5-13 


30-5 


I5-2 


IO'I 


7-60 


6-08 


5-06 


4'33 


3-78 


3-36 


3-02 


2-74 


2-50 


2-30 


2-13 


1-98 


29 


127*0 


5-23 


31-8 


I5-9 


IO'6 


7'93 


6-34 


5-27 


4-5i 


3-94 


3-50 


3-14 


2-85 


2'6l 


2' 4 C 


2'22 


2-07 


30 


132-3 


6-33 


33-i 


l6- 5 


iro 


8-26 


6-60 


5H9 


470 


4-11 


3-65 


3-27 


2-97 


2-72 


2-50 


2-32 


2-15 


31 


*377 


5-44 


34'4 


I7-2 


ii'5 


8-59 


6-87 


5-72 


4-89 


4-28 


3-79 


3'4i 


3-09 


2-83 


2-60 


2-41 


2-24 


32 


143-2 


5-55 


35-8 


17-9 


11-9 


8-94 


7' J 4 


5'95 


5-09 


4'45 


3-95 


3'54 


3-21 


2-94 


2-7I 


2-5I 


2'33 


33 


148-8 


5-69 


37-2 


18-6 


12-4 


9-29 


7-42 


6-18 


5-29 


4*62 


4'io 


3-68 


3-34 


3'06 


2'Sl 


2'60 


2-42 


34 


I54-6 


5-82 


38-6 


I9-3 


12-9 


9-65 


771 


6-42 


5'49 


4-80 


4-26 


3-83 


3-47 


3-17 


2-92 


271 


2-52 


35 


160-5 


5-96 


40-1 


2O'I 


I3-4 


IO'O 


8-00 


6-66 


5-70 


4-98 


4-42 


3-97 


3-60 


3-29 


3'03 


2'8l 


2'6l 


36 


166-5 


6-11 


4 r6 


20-8 


I3-9 


10-4 


8-30 


6-91 


5-92 


5-I7 


4*59 


412 


3-74 


3-42 


3-I5 


2-9I 


2-71 


37 


1727 


6-27 


43*2 


21-6 


14-4 


10-8 


8-61 


7-17 


6-14 


5-36 


476 


4-27 


3-88 


3-55 


3-26 


3'O2 


2-81 


38 


179-1 


6-44 


44-8 


22-4 


14-9 


II-2 


8-93 


7-43 


6-36 


5-56 


4'93 


4'43 


4-02 


3-68 


3-38 


3-I3 


2-92 


39 


185-6 


6-62 


46-4 


2 3 -2 


I5-5 


11-6 


9-26 


770 


6-60 


5-76 


5'H 


4'59 


4^7 


3-8i 


3-5I 


3-25 


3-02 


40 


192-3 


6-82 


48-1 


2 4 -0 


16-0 


12*0 


9-59 


7-98 


6-83 


5*97 


5-30 


4-76 


4'32 


3-95 


3'63 


3-37 


3-13 


4 1 


199*2 


7-03 


49'8 


2 4 -9 


16-6 


I2'4 


9'94 


8-27 


7-08 


6-19 


5'49 


4'93 


4'47 


4-09 


377 


3-49 


3-24 


4 2 


206-4 


7-26 


51-6 


25-8 


17-2 


I2'9 


10-3 


8-57 


7-33 


6-41 


5-68 


5'ii 


4-63 


4-24 


3-90 


3 -6l 


3-36 


43 


2137 


7-48 


53*4 


26-7 


17-8 


13-3 


10-7 


8-87 


7-59 


6-64 


5-89 


5-29 


4-80 


4*39 


4-04 


3-74 


3-48 


44 


221'3 


7-73 


55'3 


27-7 


18-4 


I 3 -8 


II'O 


9-19 


7-86 


6-87 


6-10 


5H8 


4-97 


4'54 


4'i8 


3-87 


3-60 


45 


229-2 


8-00 


57'3 


28-6 


19-1 


I4'3 


11-4 


9-5i 


8-14 


7-12 


6-31 


5-67 


5'i4 


470 


4-33 


.-01 


3-73 


46 


237*3 


8-29 


59*3 


29-7 


19-8 


I 4 -8 


n-8 


9-85 


8-43 


7-37 


6'54 


5-87 


5-33 


4-87 


4"49 


4-15 


3'86 


47 


245-8 


8-60 


61-4 


307 


20-5 


I5-3 


2-3 


IO'2 


873 


7" 6 3 


6-77 


6-08 


5-52 


5-05 


4-64 


4-30 


4-00 


48 


254'5 


8-93 


63-6 


3 I-8 


21'2 


I5-9 


27 


10-6 


9-05 


7-90 


7-01 


6-30 


571 


5-23 


4-81 


4-45 


4-14 


49 


263-6 


9-30 


65-9 


32-9 


22'O 


16-5 


3'i 


10-9 


9'37 


8-19 


7-26 


6-52 


5-92 


S'4 1 


4-98 


4-61 


4-29 


50 


273-1 


9-69 


68-3 


34" J 


227 


17-0 


3-6 


II'3 


971 


8-48 


7-52 


6-76 


6-13 


5'6i 


5-i6 


4-78 


4-45 


51 


283-0 


10-1 


70-7 


35'4 


2 3 -6 


177 


4'i 


117 


lO'I 


8-79 


7-80 


7-00 


6-35 


5-81 


5-35 


4-95 


4-61 


52 


293-3 


10-6 


73*3 


36-7 


24-4 


18-3 


4-6 


I2'2 


10-4 


9-11 


8-08 


7-26 


6-58 


6'O2 


5*54 


5-13 


4-78 


53 


304- 1 


11-1 


76-0 


38-0 


25-3 


19-0 


5'2 


12-6 


10-8 


9'44 


8-38 


7'53 


6-83 


6-24 


5-75 


32 


4'95 


54 


3i5'4 


11-6 


78-9 


39'4 


26-3 


19-7 


57 


I 3 'I 


II'2 


9-79 


8-69 


7-8! 


7 -08 


6-48 


5-96 


52 


5'i4 


55 


327-3 


12-2 


81-8 


40-9 


27-3 


20-4 


6-3 


13-6 


11-6 


0'2 


9-02 


8-10 


7'35 


6-72 


6-19 


"73 


5-33 


56 


339*8 


12-8 


84-9 


42-5 


28-3 


21'2 


6-9 


I 4 'I 


I2'I 


0-5 


9-36 


8-41 


7-63 


6-97 


6-42 


95 


5-53 


57 


352-9 


13-5 


88-2 


44-1 


29-4 


22-0 


7-6 


147 


I2'5 


I'O 


9-72 


8-73 


7-92 


7-24 


6-67 


6-18 


575 


58 


366-8 


14-3 


91-7 


45-8 


30-5 


22-9 


8-3 


I5-2 


I3-0 


J "4 


O'l 


9-08 


8-23 


7*53 


6-93 


6-42 


5'97 


59 


38i-4 


15-1 


95-3 


477 


31-8 


23-8 


9-0 


15-8 


13-6 


1-8 


o-5 


9-44 


8-56 


783 


7-21 


6-68 


6-21 


60 


97-0 


16-0 


99-2 


49-6 


33'0 


2 4 -8 


9-8 


16-5 


I 4 -I 


2-3 


10-9 


9-82 


8-91 


8-15 


7-50 


"95 


6-46 




m. 




m. 


m. 


m. 


m 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




59 




56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 







11 HOURS. 



When hour angle is more than 6 hours, name the factors taken from Table A tha same as the 
name of the latitude. 



13 
Table B. 

Always name the factors taken from Table B the same as the name of declination. 





HOURS. 


Decli- 


Var. 






























nation. 


tor 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m 




of 


1 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


56 




Decl. 




































































4-00 


o 


oo 


oo 


oo 


oo 


oo 


oo 


oo 


00 


oo 


oo 


oo 


oo 


oo 


oo 


I 


4-00 


4-0 


I'OO 


50 


*33 


25 


20 


17 


14 


13 


II 


10 


09 


08 


08 


07 


2 


4-01 


8-0 


2'OO 


I'OO 


67 -50 


40 


*33 


29 


*25 


22 


20 


18 


17 


16 


<:r 4 


3 


4-01 


I2'O 


3'oo 


1-50 


I'OO 


75 


60 


50 


43 


38 


'34 


30 


27 


25 


23 


'22 


4 


4-02 


16*0 


4-01 


2'OO 


i*34 


I '00 


80 


"67 


57 


'SO 


'45 


40 


'37 


'34 


'3 1 


29 


5 


4-03 


20- 1 


5-01 


2'5I 


1-67 


1-25 


I'OO 


84 


72 


'63 


*56 


'So 


46 


42 


'39 


36 


6 


4-05 


24-1 


6'02 


3-01 


2'OI 


1-51 


I-2I 


I'OI 


86 


76 


6 7 


61 


'55 


*5i 


'47 


'43 


7 


4-06 


28-1 


7-04 


3*52 


2-35 


176 


1-41 


1-17 


01 


'88 


7 8 


71 


64 


"59 


*55 




8 


4-08 


32-2 


8-05 


4-03 


2-69 


2'OI 


1-61 


i*34 


15 


01 


90 


81 


'74 


68 


62 


58 


9 


4-10 


36-3 


9-08 


4*54 


3-03 


2-27 


1-82 


1-52 


30 




I'OI 


91 


83 


76 


70 


65 


10 


412 


40-4 


lO'I 


5*05 


3'37 


2-53 


2'O2 


1-69 


'45 


27 


I-I3 


i -02 


-92 


85 


78 


73 


ii 


4-15 


44*5 


II'I 


5*57 


371 


279 


2-23 


1-86 


*59 


40 


I-2 4 


I'I2 


'02 


"93 


86 


80 


12 


4-18 


48-7 


I2'2 


6-09 


4-06 


3'5 


2*44 


2-03 


*74 


*53 


1-36 


1-22 


II 


1-02 


*94 


88 


13 


4'21 


52-9 


I 3 -2 


6-62 


4-41 


3-3I 


2-65 


2'2I 


89 


66 


I- 4 8 


i'33 


'21 


I'll 


1-03 


"95 




4'25 


57' 1 


I43 


7-14 


476 


3'57 


2-86 


2-39 


2-05 


79 


I"59 


1-44 


'3 1 


I'20 


I'll 


1-03 


15 


4-29 


6r 4 


X 5'4 


7-68 


5-12 


3-84 


3*07 


2-56 


2'2O 


*93 


171 


'54 


40 


1-29 


1-19 


i-ii 


16 


4'33 


65-7 


16-4 


8'22 




4-11 


3*29 


2-74 


2*35 


2-06 


1-83 


1-65 


50 


I- 3 8 


1-27 


1-19 


17 


4'37 


70-1 


!7*5 


876 




4-38 


3-51 


2-92 


2-5I 


2'2O 


1*95 


1-76 


60 


I- 47 


1-36 


1-26 


18 


4'42 


74-5 


18-6 


9-3I 


6-21 


4-66 


373 


3'ii 


2-6 7 


2-33 


2'08 


1-87 


70 


1-56 


1-44 


r 34 


19 


4'47 


78-9 


19-7 


9-87 


6-58 


4*94 


3'95 


3*29 


2-8 3 


2-47 


2'20 


1-98 


80 


1-66 


1-53 


1-42 


20 


4-53 


83-4 


20-9 


10-4 


6-95 


5'22 


4-18 


3-48 


2-99 


2-62 


2'33 


2'10 


91 


175 


1-62 


1-50 


21 


4'59 


88-0 


22'O 


iro 


7*33 


5*50 


4-40 


3*67 


3-15 


2-76 


2'45 


2'2I 


2'OI 


1-85 


171 


i"59 


22 


4-65 


92-6 


23*2 


n-6 


772 


5*79 


4-64 


3-87 


3*32 


2-90 


2-58 


2-33 


2'12 


1-94 


i -80 


1-67 


23 


4-72 


97-3 


24*3 


I2'2 


8-n 


6-09 


4-87 


4-06 


3'48 


3'5 


271 


2'44 


2'22 


2*04 


1-89 


i'75 


23 28' 


4-75 


99'5 


24-9 


I2'4 


8-29 


6'22 






3-56 


3'i2 


278 




2-28 


2-09 


1-93 


179 


24 


4-79 


I02'0 


25-5 


12-8 


8-51 


6- 3 8 


5'ii 


4-26 


3-65 


3-20 


2-8 5 


2' 5 6 


2*33 


2-14 


1-98 


1-84 


25 


4-87 


106-9 


26-7 


I 3'4 


8-91 


6-68 


5'35 


4-46 


3*83 


3-35 


2-98 


2-6 9 


2-44 


2-24 


2-07 


i-93 


26 


4-95 


m-8 


27-9 


14-0 


9-32 


6-99 


5-60 


4-67 


4'OO 


3'5Q 


3'12 


2'8l 


2-56 


2-35 


2-17 


2'O2 


27 


5-04 


116-8 


29-2 


! 4 '6 


974 


7*30 


5-85 




4 -l8 


3'66 


3-26 


2-93 


2-67 


2*45 


2-27 


2'II 


28 


5'13 


121-9 


30-5 


15*2 


I0'2 


7-62 


6'io 


5*09 




3-82 


3'4 


3-06 


279 


2-56 


2-36 


2'2O 


29 


5'23 


127-0 


31-8 


I5-9 


10-6 


7-95 


6-36 


5-30 


4-55 


3-98 


3-54 


3*19 


2-91 


2-67 


2-46 


2'29 


30 


5'33 


132-3 


33' 1 


16-5 


II'O 


8-28 


6-62 




4*74 


4*i5 


3-69 






278 


2'57 


2-39 


Names of Stars. 
































N. Decln. Stars. 
































Procyon 


21-9 


5*47 


2-74 


1-83 


i'37 


I'lO 


91 


78 


69 


61 


*55 


50 


46 


42 


*39 


Altair 


34-8 


8-69 


4'35 


2-90 


2'l8 


i*74 


i-45 


1-25 


1-09 


*97 


87 


80 


73 


67 




Aldebaran . . 


67-1 


16-8 


8-39 


5*6o 


4-20 


3-36 


2-80 


2-40 




1-87 


1-69 


i*54 


1-41 


1-30 


I'2I 


Arcturus 


81-9 


20-5 


10-2 


6-82 


5-12 


4-10 


3'4 2 


2-93 


2-57 


2-28 


2-06 


1-87 


172 


1-59 


I' 4 8 


Castor 


I43-7 


35-9 


I 7 '8 


I2'O 


8-99 


7-19 


6 - oo 


5-I4 


4-51 


4-01 


3"6i 


3*29 


3*02 


2-79 


2-59 


Vega 


183-6 


45-9 


23*0 


I 5'3 


"5 


9-19 


7-66 


6-57 


576 


5'12 


4-61 


4-20 


3-85 


3*56 


3*31 


Deneb 


228-9 


57*2 


28'6 


19-1 




n*5 


9*55 


8-19 


7-17 


6-38 


5*75 


5-23 


4-80 


4*44 


4* X 3 


Capella 


236-6 


59-i 


29-6 


197 


14-8 


ii'8 


9-87 


8-47 


7*42 


6-60 


5-94 




4*96 


4*59 


4*27 


a Persei 


268-7 


67-2 


33-6 


22-4 


16-8 




ira 


9-62 


8-43 


7-50 


6-75 


6-15 


5*64 


5-21 


4*85 


t\ Ursae Majoris 


270-8 


677 


33-9 


22-6 


i6'9 


13-6 


11-3 


9-70 


8'49 


7*55 


6-81 


6-19 


5-68 


5-25 


4*89 


e Ursae Majoris 


345*6 


86-4 


43*2 


28-8 


21-6 


17-3 


14-4 


12-4 


io-8 


9*64 


8-68 


7-90 


7*25 


6-70 


6-23 


a Ursae Majoris 


435'4 


109 


54-4 


36-3 


27-2 


21'8 


18-2 


15-6 


13-6 


I2'I 


10-9 


9*96 


9-14 


8*44 


7*85 


S. Decln. Stars. 
































Rigel 


33*5 


8-36 


4-18 


2*79 


2-09 


1-67 


I '40 


I '20 


1-05 


93 


84 


*77 


70 


65 


60 


Sirius 


68-3 


17-1 


8'54 


5-69 


4-27 




2-85 


2-44 


2-14 


I-9I 


172 


1-56 


i'43 


1-32 


1-23 


e Sagittarii . . 


157*1 




i9'6 




9*83 


7-86 


6-56 


5-62 


4-92 


4-38 


3*95 


3-59 


3-30 




2-83 


X Scorpii 


172-9 


43*2 


21'6 


I4'4 


10-8 


8-66 


7-22 


6-19 


5*42 


4 -82 


4*35 


3-95 


3-63 




3-12 


y Argus 


246-4 


61-6 


30-8 


20'5 


15*4 


I2'3 


10-3 


8-82 


772 


6-8 7 


6*19 


5-63 


5*17 


478 


4*44 


a Gruis 


249-2 


62-3 


31-2 


20'8 


15-6 


12-5 


10-4 


8-92 


7-81 


6-95 


6-26 


57 


5-23 


4*83 


4*49 


Canopus 


300-3 




37'5 


25-0 


18-8 


15-0 


12-5 


10-8 


9-41 


8-38 


7*54 


6-87 


6-30 


5-82 


5-42 


y Crucis 


347*7 


86-9 


43*5 


29-0 


217 




14-5 


12-4 


10-9 


970 


8-74 


7*95 


7*30 


674 


6-27 


a Pavonis 


353-2 


88-3 


44*2 


29*4 


22'I 


177 


147 


I2'6 


ii'i 


9-85 


8-88 


8-08 


7-41 


6-85 


6-37 


Achernar . . 


362-4 


90-6 


45*3 


30-3 


22'7 


18-1 




13-0 


11-4 


lO'I 


9-11 


8-29 


7-61 


7*03 


6-54 


ft Crucis or ) 
e Argus / 


384-6 


96-2 


48-1 


32-1 


2 4 -I 


19*3 


16-1 


13-8 


I2'I 


107- 


9-66 


879 


8-07 


7-46 


6-94 


ft Centauri 


396-0 


99-0 


49*5 


33-0 


24-8 


19-8 


16-5 


14-2 


I2' 4 


II'O 


9'95 


9*06 


8-31 


7-68 


7 <]C 4 


a 2 Centauri 


44'5 


IOI 


50*6 


337 


25-3 


20'2 


16-9 




I2'7 


11-3 


IO'2 


9' 2 5 


8-49 


7*85 


7'3 


a 1 Crucis 


442-1 


in 


55*3 




27*7 


22'I 


18-5 


15*8 


I3-9 


12-3 


II'I 


IO'I 


9-28 


8-58 


7'97 


a TrianguliAus 


592-8 


148 


74*i 


49'4 


37* 1 


29*7 


247 


21'2 


18-6 


16-5 


14-9 


13-6 


12-4 


ii*5 


10-7 


ft Argus 


608-0 




76-0 


50-7 


38-0 


30*4 


25-4 


21-8 


19-1 


17-0 


I5-3 


I3-9 


I2'8 


ii'8 


II 




m. 


m. 


m. I m. 


m. 


m. 


m. m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




59 




52 ! 48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 




11 HOURS. 



Table A. 

When hour angle is less than 6 hours, name the factors taken from Table A contrary to name of lat. 





1 HOUR. 


2 Hr. 


Lat. 


m. 


m. 


m. 


m. 


m. 


in. 


m. 


m. 


in. m. 


m. 


m. 


m. 


m. 


m. 


m. 







4 


8 


12 


1C 


20 


24 


28 


32 36 


40 


44 


48 


52 


56 


00 











j 




























O 


oo 


oo 


oo 


oo 


oo 


00 


'OO 


00 


00 


oo 


oo 


oo 


oo 


oo 


oo 


oo 


I 


07 


06 


06 


'5 


'05 


'OS 


'05 


04 


04 


04 


04 


04 


03 


03 


03 


03 


2 


13 


12 


II 


ii 


'IO 


10 


09 


09 


08 


08 


07 


07 


07 


07 


06 


06 


3 


20 


18 


17 


16 


15 


'14 


14 


13 


'12 


'12 


II 


II 


10 


10 


09 


09 


4 


26 


24 


23 


22 


'20 


19 


18 


17 


16 


16 


15 


14 


14 


13 


13 


'12 


5 


'33 


'3i 


29 


27 


'25 


24 


23 


'22 


'21 


20 


19 


18 


17 


16 


16 


-I 5 


6 


39 


'37 


34 


3 2 


31 


29 


27 


26 


'25 


24 


23 


'22 


21 


20 


19 


18 


7 


4 6 


'43 


40 


38 


36 


'34 


32 


3 


29 


28 


26 


25 


24 


'23 


22 


21 


8 


'52 


'49 


46 


'43 




'39 


'37 


'35 


'33 


32 


30 


29 


28 


26 


'25 


24 


9 


'59 


'55 


52 


'49 


46 


'44 


41 


'39 


'37 


36 


34 


32 


31 


30 


29 


27 


10 


66 


61 


58 


'54 


'5i 


48 


46 


'44 


42 


40 


-38 


36 


'35 


33 


32 


'31 


ii 

12 


73 
79 


68 
74 


64 
70 


60 
'65 


56 
62 


'53 

58 


'55 


48 
'53 


4 6 
'50 


3 


42 

46 


4 

'44 


38 
42 


'37 
40 


'35 
38 


'34 

'37 


13 


86 


81 


76 


71 


67 


'63 


60 


'57 


'54 


52 


50 


'47 


'45 


'43 


'42 


40 


14 


'93 


87 


82 


77 


72 


69 


'65 


62 


'59 


56 


53 


'Si 


'49 


'47 


'45 


'43 


15 


I'OO 


'93 


88 


82 


78 


74 


70 


66 


'63 


60 


'57 


'55 


53 


50 


48 


46 


16 


1-07 


I'OO 


'94 


88 


83 


79 


75 


71 


68 


64 


61 


'59 


56 


'54 


52 


'50 


17 


1-14 


1-07 


I'OO 


'94 


89 


84 


80 


7 6 


72 


69 


66 


'63 


60 


57l '55 


'53 


18 


I'2I 


1-13 


06 


I'OO 


94 


89 


85 


80 


77 


73 


70 


67 


64 


61 


59 


56 


19 


1-29 


I'20 


'13 


i -06 


I'OO 


95 


90 


8 5 


81 


77 


74 


7i 


68 


65 


62 


60 


20 


1-36 


I'27 


19 


I'I2 


i -06 


I 00 


95 


90 


86 


82 


78| 75 


7i 


68 


66 


63 


21 


*'43 


I'34 


26 


1-18 


I'll 


1-05 


100 95 


90 


86 


82J 79 


75 


72! -69 


66 


22 




I' 4 I 


32 


1-24 


1-17 




1-05 


i -oo -95 


91 


'87! '83 


79 


76! 73 


70 


23 


1.45 


I' 4 8 


'39 


1-31 


1-23 


1-17 


i'ii 


1-05) i -oo 


'95 


91] '87 


83 


80 


77 


74 


24 


1-66 




46 




1-29 


I '22 


1-16 


1'ioj 1*05 


I'OO 


'951 '9i 


87 


84 


80 


77 


25 


174 


I-6 3 


'53 


i -44 


i'35 


1-28 I -21 


1-15 no 


i 5 


i-ooj -96 


92 


88 


84 


Si 


26 


1-82 


170 


60 


1-50 


1-42 


i '34 


1-27 


I'2I 


1-15 


no 


1-05 i -oo 


96 


92 


88 


84 


27 


i '90 


I- 7 8 


67 




1-48 


i '40 


i 33 


1-26 


I '20 


1-14 


1-09 


1-04 


I'OO 


96 


92 


88 


28 


1-98 


I-8 5 


74 


1-64 


i '54 


1-46 


i '39 


1-32 


1-25 


1-19 


1-14 


1-09 


i '04 


I'OO 


96 


92 


29 


2-07 


i '93 


81 


171 


i'6i 


1-52 


1-44 


i '37 




1-24 


rig 




i -09 


1-04 


I'OO 


96 


30 


2-15 


2'OI 


89 


178 


1-68 


i '59 


1-50 


i '43 


1-36 


1-30 


1-24 


1-18 


1-13 


1-09 


1-04 


I'OO 


31 


2-24 


2'IO 


1-97 


1-85 


i'75 


i'65 


1 '57 


1-49 


I-42 


i- 35 


1-29 


1-23 


1-18 


1-13 


i -08 


1-04 


32 


2'33 


2'l8 


2-04 


i '92 


1-81 


172 


1-63 


i '55 


i '47 


1-40 


i'34 


1-28 


1-23 


1-18 


1-13 


i -08 


33 


2-42 


2-26 


2'12 


2'OO 


1-89 


178 


1-69 


r6i 


i'53 


1-46 


i '39 


i'33 


1-27 


I'22 


1-17 


I'I2 


34 


2-52 


2'35 


2'2I 


2-08 1-96 


1-85 


176 


1-67 


i '59 


1*51 


i '45 


1-38 


1-32 


I-2 7 


I'22 


I ' I 7 


35 


2'6l 




2'29 


2'l6 


2-03 


1-92 


1-82 


173 


1-65 


i'57 


1-50 


1-44 


i '37 


I-32 


1-26 


I'2I 


36 


271 


2'53 


2-38 


2-24 


2'II 


2'OO 


1-89 


i -80 


171 


1-63 


1-56 


1-49 


i '43 


i '37 


I'3I 


1-26 


37 


2'8l 


2'6 3 


2- 4 6 


2-32 


2'19 


2'07 


1-96 


1-87 


178! 1-69 


1-62 




1-48 


1-42 


1-36 


I-3I 


38 


2-92 


272 




2-40 


2'27 


2'15 


2-04 


i '93 


1-84 


175 


1-68 


i -60 


1*53 


1-47 


I'4I 


i'35 


39 


3-02 


2'82 


2-65 


2-49 


2'35 


2'22 


2'II 


2'OO 


1-91 


1-82 


174 


1-66 


i'59 


1-52 


I' 4 6 


1-40 


40 


3-I3 


2'93 


274 


2-58 


2*44 


2-3I 


2-19 


2'08 


1-98 


1-88 


i -80 


172 


i -65 


1-58 






4 1 


3'24 


3'3 


2-84 


2-68 


2-52 


2-39 


2'26 


2'15 


2-05 


i '95 


1-86 


178 


171 


1-63 


J< 57 


I '5 I 


42 


3'36 


3'i4 


2'95 


277 


2'6l 


2-47 


2'35 


2'23 


2'12 


2 '02 


i '93 




177 


1-69 


1-62 


1-56 


43 


3'48 


3'25 


3'05 


2-87 


271 


2-56 


2'43 


2-3I 


2'20 


2-09 


2'OO 


1-91 


1-83 


I- 75 


1-68 


1-62 


44 




3'37 




2'97 


2'80 


2*65 


2-52 


2-39 


2'28 


2-17 


2-07 


1-98 


1-90 


1-82 


174 


1-67 


45 


373 


3'49 


3'27 


3'o8 


2 '9O 


275 


2'6l 


2-48 


2-36 


2-25 


2-14 


2-05 


i '96 


1-88 


i -80 




46 


3'86 


3'6i 


3'39 


3'i9 


3-01 


2-85 


270 


2-56 


2-44 


233 


2'22 


2'12 


2-03 


i '95 


1-87 


179 


47 


4-00 


374 


3'5i 


3'30 


3*11 


2-95 


279 


2*65 


2'53 


2' 4 I 


2-30 


2'2O 


2'10 


2'O2 


i '93 


1-86 


48 


4-14 




3*63 


3*42 


3'23 


3 '05 


2-89 


275 


2'62 




2-38 


2-28 


2-18 


2'09 


2'OO 


1-92 


49 


4-29 


4-01 


376 


3'54 


3'34 




3-00 


2*85 


271 


2'58 


2-47 


2-36 


2-26 


2'l6 


2'08 


1-99 


50 


4'45 


4-16 


3-90 


3 '6 7 


3'4 6 


3'27 


3'io 


2-95 


2'8l 


2-68 




2-44 


2'34 


2-2 4 


2'15 


2-06 


51 


4-61 


4'3 J 


4-04 


3'8o 


3'59 


3'39 


3-22 


3'o6 


2-9I 


277 


2'6 5 


2'53 


2-42 


2-32 


2'2 3 


2-14 


52 


478 


4-46 


4-19 


3'94 


372 




3'33 


3'i7 


3 -02 


2-87 


274 


2-62 


2-51 


2-41 


2- 3 I 


2'22 


53 


4'95 




4'34 


4-08 


3'85 


3-65 




3'28 




2-98 




272 


2-60 


2-50 


2-39 


2-30 


54 


5-I4 


4-80 


4'5o 


4-24 


4-00 


378| 3'59 


3'4 J 


3' 2 4 


3-09 


2'95 


2-82 


270 


2'59 


2-48 




55 


5'33 


4-98 


4-67 


4-40 


4^5 


3-92 


372 


3'53 


3'36 


3'2I 


3-06 


2'93 


2-80 


2-69 


2' 5 S 


2-47 


56 


5'53 


5-17 


4'85 


4-56 


4-31 


4-07 


3-86 


3'67 


3*49 


3'33 


3'l8 


3'04 


2-91 


279 


2-67 


2'57 


57 


575 


5'37 


5 '04 


474 


4*47 


4' 2 3 


4 - oi 


3'8i 


3'63 


3'46 


3'3 




3-02 


2-90 


278 


2-6 7 


58 


5'97 


5'58 


5'23 


4'93 


4;65 


4'4 


4-17 


3'96 


377 


3'59 


3'43 


3*28 


3' 1 4 


3-01 


2-89 


277 


59 


6'2I 




5'44 






4'57 


4'34 


4-12 


3-92 


374 


3'57 


3'4 J 


3'27 


3'i3 


3-00 


2-88 


60 


6-46 


6-04 




5'33 


5'3 


476 




4-29 


4-08 




371 


3'55 


3'40 


3-26 


3-12 


3'oo 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 1 m. i m. 


m. 


m. 




oo 


56 


5 2 


48 


44 


40 


36 


32 


28 


24 


20 


16 , 12 8 


4 


00 




11 HR. 


10 HOURS. 



When hour angle is 
the name of latitude. 



more than 6 hours, name the factors taken from Table A the same a* 



Table B. 

Always name the factors taken from Table B the same as the name of declination. 





1 HOUR. 


2Hr. 


Declination. 




































m. 


m. 


in. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




00 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 




O 






y, 


























oo 


oo 


oo 


oo 


00 


oo 


oo 


oo 


oo 


00 


oo 


oo 


oo 


oo 


oo 


I 


07 


06 


06 


05 


'05 


'05 


'05 


4 


04 


04 


04 


04 


04 


04 


03 


2 


13 


13 


12 'II 


ii 


10 


10 


09 


09 


09 


08 


08 


08 


07 


07 


07 


3 


20 


19 


IS -17 


16 


15 


15 


'14 


13 


13 


12 


12 


'12 


II 


II 


10 


4 


27 


25 


24 


23 


21 


20 


20 


19 


18 


17 


17 


16 


15 


'IS 


14 


<J 4 


5 


'34 


32 


30 


28 


27 


26 


24 


23 


'22 


22 


'21 


'20 


19 


19 


18 


17 


6 


41 


38 


36 


'34 


32 


31 


29 


28 


27 


26 


25 


24 


23 


*22 


'22 


21 


7 


'47 


45 


42 


40 


38 


3 6 


34 




'3 1 


3 


29 


'28 


27 


26 


'25 


'25 


8 


'54 


51 


48 


;45 


'43 




39 




36 


'35 


'33 


32 




3 


29 


28 


9 


61 


57 


54 




'49 


46 


44 


42 


'41 


'39 


'37 


36 


"35 


'34 


'33 


32 


10 


68 


64 


60 


57 


'54 


'52 


49 


'47 


'45 


'43 


42 


'40 


'39 


38 


36 


'35 


ii 


75 


71 


66 


6 3 


60 


'57 


54 


52 


'SO 


48 


4 6 


'44 


'43 


'4 1 


40 


'39 


12 


82 


77 


73 


6 9 


'65 


62 


59 


'57 


"54 


52 


'50 


48 


'47 


'45 


'44 


'43 


13 


89 


84 


79 


75 


71 


68 


64 


62 


'59 


57 


'55 


'53 


'51 


'49 


48 


46 




96 


90 


85 


81 


77 


73 


70 


67 


64 


61 


'59 


'57 


'55 


'53 


'51 


'50 


15 


1-04 


'97 


92 


'87 


82 


78 


75 


72 


69 


66 


63 


61 


'59 


57 


*55 


'54 


16 


i'i i 


1-04 


98 


'93 


88 


84 


80 


77 


73 


70 


68 


65 


63 


61 


'59 


57 


jy 


1-18 


I'll 


1-05 


99 


'94 


89 


'85 


82 


78 


75 


72 


70 


67 


65 


"63 


61 


18 


1-26 


n8 




1-05 


I'OO 


95 


91 


87 


'83 


80 


77 


74 


72 


69 


67 


65 


19 


i'33 


1*25 


n8 


i'ii 


i -06 


I '01 


96 


92 


88 


'85 


81 


79 


76 


73 


71 


69 


20 


1-41 


1-32 


1-24 


1-18 


I'I2 


i -06 


I'O2 


'97 


'93 


'89 


86 


83 


80 


78 


75 


73 


21 


1-48 


J '39 


I'M 


24 


1-18 


'12 


07 


I '02 


98 


'94 


9i 


88 


85 


82 


79 


77 


22 


1-56 


1-47 


I- 3 8 




1-24 


18 


13 


I -08 


1*03 


99 


96 


92 


89 


86 


'83 


81 


23 


1-64 






'37 


1-30 


24 


18 


I-I3 


1-09 


04 


I -00 


'97 


93 


90 


88 


'85 


23 28' 


1-68 


i'57 


1-48 


40 




27 


'21 


1-16 


ii 


07 


i 03 


'99 


96 


92 


90 


'87 


24 


1-72 


1-62 


1-52 


'44 


I- 37 


30 


24 


1-19 


'14 


09 


I'Oj 


02 


98 


95 


92 


'89 


25 


i -80 


1-69 


i '59 




i '43 


36 


3 


1-24 


19 


'15 


I 10 


06 


1-03 


99 


96 


'93 


26 


1-88 


1-77 


1-67 


1-58 


1-50 


'43 


36 


1-30 


'25 


'20 


I 15 


ii 


1-07 


1-04 


I'OI 


98 


27 


1-97 


1-85 


174 


1-65 


J '57 


'49 


42 


1-36 


30 


25 


I'2I 


16 




1-09 


1-05 


I '02 


28 


2*05 


i'93 


1-82 


172 


i'6 3 


'55 


48 


1-42 


36 


'31 


1-26 


21 


1*17 


1*13 


no 


I 'O6 


29 


2-14 


2'OI 


1-90 


179 


170 


62 


'55 


r 4 8 


42 


I- 3 6 


I-3I 


26 


I'22 


n8 


1-14 


I'll 


30 


2*23 


2-09 


1-97 


1-87 


177 


69 


1-61 


i '54 


48 


I- 4 2 


i '37 


32 


1-27 


1*23 


1-19 


i'i5 


Stars. 


































N.Decln. 


































Procyon 


'37 


'35 


'33 


31 


29 


28 


27 


26 


24 


23 


23 


22 


21 


20 


20 


19 


Altair . . 


'59 


'55 


'52 


'49 


'47 


'45 


42 


41 


'39 


37 


36 


'35 


'33 


'32 


31 


'3 1 


Aldebar'n 


i - i3 


I -06 


I -00 


95 


90 


86 


82 


78 


75 


72 


69 


67 


65 


62 


60 


'59 


Arcturus 


1-38 


I- 3 


I'22 


1-16 


no 


1-04 


I'OO 


'95 


91 


88 


84 


81 


79 


76 


74 


71 


Castor . . 


2-42 


2-27 


2-14 


2-03 


i '93 


1-83 


175 


1-67 


i -60 


i'54 


i- 4 8 


i '43 


1-38 


I'34 


1-29 


i 25 


Vega . . 


3-10 


2-9I 


2'74 


2'59 


2-46 


2-34 


2-24 


2-14 


2-05 


1-97 


1-90 


i'8 3 


176 


171 


1-65 


i -60 


Deneb .. 


3'86 


3-62 


3'42 


3'23 


3-07 


2-92 


279 


2-67 


2-56 


2-46 


2-36 


2-28 


2'2O 




206 


2'OO 


Capella 


3'99 


374 


3'53 


3'34 




3-02 


2-88 


276 


2-64 


2'54 


2'44 


2'35 


2-27 


2'20 


2 13 


2'06 


a Persei . . 


4'53 




4'01 


379 


3-6o 


3'43 


3-27 


3-13 


3-00 


2-88 


277 


2-67 


2-58 


2-50 


2- 4 2 


2'35 


rj Ursae Maj. 


4'57 


4-29 


4-04 


3'82 


3-63 


3-46 


3-29 


3' J 5 


3-02 


2-90 


2-80 


270 


2'60 


2-52 


2 '44 


2- 3 6 


eUrsaeMaj. 




5 '47 




4-88 


4' 6 3 


4-41 


4-21 


4'3 




371 


3'57 


3'44 


3'32 


3'2I 


3-11 


3 -02 


aUrsasMaj. 


7'34 


6-89 


6-50 


6-15 


5'83 


5'55 


5-30 


5'<>7 


4-86 


4-67 


4-50 


4'33 


4-18 


4'5 


3-92 


3'80 


S. Decln. 


































Rigel .. 


56 


'53 


'49 


'47 


'45 


'43 


'4 1 


'39 


'37 


36 


'35 


33 


32 


'3 1 


30 


29 


Sirius .. 




i -08 


I'O2 


96 


92 


'87 


83 


80 


76 


73 


7 1 


68 


66 


'63 


61 


60 


e Sagittarii 


2-65 


2-49 


2'34 


2'22 


2-n 


2'OO 


1-91 


1-83 


175 


1-68 


1-62 


1-56 


1*51 


1-46 


141 


I'37 


X Scorpii 


2-92 


274 




2-44 


3'32 


2-21 


2'II 


2'OI 


i '93 


1-86 


179 


172 


1-66 


1-61 


1-56 


I '5 I 


7 Argus . . 


4' J 5 


3-90 


3'68 


3- 4 8 


3'30 


3-I4 


3'00 


2-8 7 


275 


2'6 4 


2'54 


2 '45 


2'37 


2*29 


2'22 


1-15 


a Gruis . . 


4-20 


3'94 


372 


3'52 


3'34 


3'i8 


3-03 


2'90 


278 


2-67 


2'57 


2-48 


2-40 


2-32 


2-24 


2-17 


Canopus 


5-o6 


475 




4-24 


4-02 


3'8 3 


3-66 




3'35 


3'22 


3-10 


2-99 


2-89 


279 


270 


2-62 


7 Crucis . . 


5'86 




5'i9 


4-91 


4-66 


4'44 


4'23 


4'5 


3-88 


373 


3'59 


3 '46 


3'34 


3' 2 3 


3 -I 3 


3'3 


a Pavonis 
Achernar 


6-n 


5'59 
574 


5'4i 


4'99 

5'12 


473 
4-86 


4-62 


4'30 
4-41 


4-11 
4-22 


3'94 
4'5 


379 
3-89 


3'65 
374 


PI 


3-40 
3'48 


3'28 
3'37 


3'i8 
3-26 


3-08 
3-16 


/3 Crucis J 
e Argus j 


6-48 


6*09 


574 


5'43 


5'*5 


4-91 


4-68 


4-48 


4-29 


4 -I 3 


3'97 


3-83 


37 


3'57 


3H6 


3-36 


/3 Centauri 


6-68 


6-27 


S'9 1 


5'59 




5'5 


4-82 


4-61 


4-42 


4'25 


4-09 


3-94 


3'8i 




3-56 


3'46 


a 2 Centauri 


6-82 


6-40 


6-04 


57 1 


5'42 




4-92 


471 


4'52 


4'34 


4-18 


4'3 


3'89 


376 


3'64 


3'53 


a 1 Crucis . . 


7'45 


7-00 


6'6o 


6-24 


5'93 


5*64 




5'i5 


4'93 


474 


4'57 


4-40 


4-25 


4-11 


3'98 


3'86 


a Tri. Aus. 


9-99 


938 


8-85 


8'37 


7'95 


7'56 


7-22 


6-91 


6-62 


6-36 


6'12 


5'9 


57 


5'5i 


5'34 


5'i7 


/3Argu? .. 


10-25 


9-62 


9-07 


8' TO 


8-15 


775 


7-40 


7-08 


679 


6-52 


6-28 


6-05) 5' 8 4 


5-65 


5'47 


5'3i 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




00 


56 


52 


48 


44 


40 


36 


3 2 


28 


24 


20 


16 


12 


8 


4 


00 




11 Hr. 


10 HOURS. 



IS 



Table A. 

When hour angle is less than 6 hours, name the factors taken from Table A contrary to name of lat. 





2 HOURS. 


3 Hr. 


Lat. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


in. 


m. 


m. 


in. 


m. 


m. 


111. 


m. 


m. 




00 


4 


8 


12 


16 


20 


24 


28 


32 


86 


40 


44 


48 


52 


56 


00 





00 


oo 


OO 


oo 


oo 


oo 


OO 


00 


oo 


oo 


oo 


oo 


oo 


00 


oo 


oo 


I 


03 


03 


03 


03 


03 


02 


02 


O2 


O2 


02 


02 


O2 


02 


02 


'02 


02 


2 


06 


06 


06 


05 


05 


05 


05 


05 


4 


4 


04 


04 


4 


04 


04 


03 


3 


09 


09 


08 


08 


08 


07 


07 


07 


07 


06 


06 


06 


06 


06 


05 


05 


4 


12 


'12 


II 


II 


10 


10 


10 


09 


09 


09 


08 


08 


08 


07 


07 


07 


5 


'IS 


* X 5 


' I 4 


13 


13 


12 


12 


12 


II 


II 


10 


10 


10 


09 


09 


09 


6 


18 


' I 7 


17 


16 


16 


15 


I 4 


14 


13 


13 


13 


'12 


12 


II 


II 


ii 


7 


21 


20 


20 


19 


18 


18 


17 


16 


16 


'IS 




' J 4 


14 


'13 


" J 3 


12 


8 


24 


23 


'22 


'22 


21 


20 


19 


19 


18 




17 


16 


16 


15 


15 


14 


9 


'27 


26 


25 


24 


23 


23 


'22 


, .ji 


20 


2O 


19 


18 


18 


17 


16 


16 


10 




29 


28 


27 


'26 


25 


2 4 


23 


23 


'22 


21 


20 


20 


19 


18 


18 


ii 


'34 


32 


31 


3 


29 


28 


27 


'26 


25 


2 4 


23 


'22 


'22 


'21 


'20 


19 


12 


*37 


'35 


'34 


'33 


32 


30 


29 


28 


27 


'26 


25 


24 


24 


23 


'22 


21 


13 


4 


;ss 


'37 


36 


'34 


*33 


32 


"3 1 


30 


29 


28 


27 


26 


25 


24 


23 




"43 




4 


; 3 8 


'37 


36 


'34 


'33 


32 


'3 1 


30 


29 


28 


27 


26 


'25 


15 


46 


'45 


'43 




4 


38 


'37 


36 


'34 


'33 


32 




30 


29 


28 


27 


16 


'SO 


4 i 


46 


'44 


'43 


41 


'39 


38 


'37 


'35 


34 


'33 


32 


'3 1 


3 


'29 


17 


'53 




'49 


47 


'45 


'44 


42 


41 


'39 


38 


36 


35 


'34 


33 


32 




18 


56 


54 


52 


50 


4 8 


46 


'45 


'43 


42 


40 


39 


'37 


3 6 


'35 


'34 


32 


19 


60 


'57 


'55 


53 


51 


'49 


'47 


46 


'44 


'43 


4! 


4 


38 


'37 


36 


'34 


20 


6 3 


61 


58 


56 


'54 


52 


'SO 


48 


'47 


'45 


'43 




4 


'39 


38 


36 


21 


66 


64 


61 


59 


57 


'55 


53 


51 


49 


47 


4 6 


'44 


'43 


'4 1 


40 


38 


22 


70 




65 


62 


60 


58 


56 


'54 


'52 


'SO 


: 4 ? 


46 


*45 


'43 


42 


'40 


23 


74 


7 


68 


65 


6 3 


61 


58 


56 


'54 


52 




'49 


'47 


46 


'44 


42 


24 


77 


74 


7 1 


69 


66 


64 


61 


59 


"57 


'55 


53 




'49 


48 


46 


'45 


25 


81 


78 


75 


72 


69 


67 


64 


62 


60 


58 


56 


'54 


'52 


'50 


4 8 


'47 


26 


84 


81 


78 


75 


72 


70 


-67 


65 


62 


60 


58 


56 


'54 


52 


5 I 


'49 


27 


88 


85 


82 


78 


76 


73 


70 


68 


'65 


63 


61 


'59 


'57 


'55 


'53 




28 


92 


88 


85 


82 


79 


76 


73 


71 


68 


66 


63 


61 


59 


'57 


'55 


'53 


29 


96 


92 


89 


85 


82 


79 


76 


74 


71 


68 


66 


64 


62 


'59 


'57 


'55 


30 


I -00 


96 


92 


89 


86 


82 


79 


77 


74 


71 


69 


66 


64 


62 


60 


58 


31 


04 


I'OO 


96 


'93 


89 


86 


83 


80 


77 


74 


72 


69 


67 


64 


62 


60 


32 


08 


1-04 


I'OO 


96 


'93 


89 


86 


83 


80 


77 


74 


72 


69 


67 


65 


62 


33 


I'I2 


i -08 


1-04 


I -00 


96 


'93 


89 


86 


83 


80 


77 


75 


72 


70 


6 7 


'65 


34 


17 


I'I2 


i -08 


i '04 


I'OO 


96 


'93 


90 


86 


8 3 


80 


78 


75 


72 


70 


67 


35 


'21 


I'I7 


I'I2 


i -08 


1-04 


I'OO 


96 


'93 


90 


86 


83 


81 


78 


75 


73 


70 


36 


26 


I'2I 


i 16 


I-I2 


i -08 


1-04 


I -00 


96 


'93 


90 


87 


'84 


81 


78 


75 


73 


37 


'3 1 


1-25 


I'2I 


1-16 


I'I2 


i 08 


1*04 


I'OO 


96 


'93 


90 


87 


84 


81 


78 


75 


38 


'35 


I' 3 


1-25 


I'2O 


1-16 


I'I2 


i -08 


1-04 


I'OO 


96 


93 


90 


87 


84 


81 


78 


39 


40 




I' 3 


1-25 


I'2O 


ri6 


I'll 


1-07 


1-04 


I -00 


97 


'93 


90 


87 


84 


81 


40 


'45 


I'40 


i '34 


1-29 


I'24 


I'20 


J **5 


i'ii 


1-07 


i -04 


I'OO 


'97 


'93 


90 


87 


84 


41 


51 


i '45 


i '39 


1-34 


I'2 9 


1-24 


I'2O 


1-15 


i-ii 


1-07 


1-04 


oo 


'97 


'93 


90 


87 


42 


56 


1-50 


i -44 


1*39 




1-29 


1-24 


1-19 


1 ' 1 5 




1-07 


04 


I'OO 


97 


'93 


go 


43 


62 




i -49 


1-44 


I'll 




1-28 


1-24 


1-19 


I ' I 5 




07 


i '04 


I'OO 


'97 


'93 


44 


67 


1-61 


1 '55 


I'49 


i '43 


I'll 


i '33 


1-28 


1-24 


1-19 


15 


ii 


1-07 


1-04 


I'OO 


97 


45 


73 


i'66 


i -60 




1-48 




1-38 


i '33 


1-28 


1-23 


19 


15 




1-07 


1-04 


I'OO 


46 


79 

.Of. 


172 

r*tmQ 


1-66 


T'fic 


J '54 


1-48 




i-37 


i '33 


1-28 


23 

78 


19 


1*15 


ii 


07 


04 


47 

48 


oo 

1-92 


I 70 

1-85 


172 

178 


1 5 
171 


1-65 


i'59 


i'53 


1-47 


1-42 




20 
32 


"23 

28 


1-2^ 


* I f 

19 


" 1 1 

15 


07 
II 


49 


1-99 


1-91 


1-84 


177 


171 


1-64 


1-58 




1-47 


1-42 


'37 


32 


1-28 


2 , 


19 


15 


50 


2-06 


!' 9 8 


1-91 


I'8 4 


177 


170 


1-64 


1-58 


i '53 


i '47 


42 


37 


1-32 


28 


23 


19 


51 


2-14 


2 '06 


1-98 


I'90 


1-83 


176 


170 


1*64 


i '58 


1-52 


'47 


42 


i'37 


32 


28 


23 


52 


2'22 


2'13 


2-05 


I'97 


1-90 


1-83 


176 


170 


1-64 


1-58 


'53 


'47 


1-42 


'37 


'33 


28 


53 


2-30 


2'2I 


2'12 


2-04 


1-97 


1-90 


1-83 


176 


170 


1-64 


58 


53 


i '47 


42 


'37 


33 


54 


2-38 


2-29 


2'2O 


2'12 


2-04 


i -97 


1-89 


1-83 


176 


170 


64 


58 


i '53 


48 


'43 


38 


55 


2-47 




2-29 


2'20 


2'12 


2*04 


1-97 


1-90 


1-83 


176 


70 


64 


i'59 


53 


48 


43 


56 


2'57 


2-47 


2'37 


2-28 


2'20 


2'12 


2 '04 


1-97 


1-90 


1-83 


77 


71 


1-65 


'59 


'54 


48 


57 


2-6 7 




2' 4 6 


2-37 


2'28 


2'2O 


2'12 


2 '04 


1-97 


1-90 


8 4 


77 


171 


65 


59 


54 


58 


277 


2-66 


2' 5 6 


2-46 


2'37 


2-29 


2'20 


2-12 


2-05 


1-98 


1-91 


84 


178 


72 


66 


60 


59 


2-88 


277 


2'66 


2-56 


2-47 


2' 3 8 


2'29 


2'2I 


2-13 


2-06 


1-98 


91 


1-85 


78 


72 


66 


60 


3 -oo 


2-88 


277 


2'6 7 


2'57 




2' 3 8 


2'30 


2*22 


2-14 


2-06 


99 


1-92 


1-86 


179 


73 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. I m. 


m. 


m. 




oo 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 1 8 


4 


00 




10 Hr. 


9 HOURS. 



When hour angle is 
the name of the latitude. 



more than 6 hours, name the factors taken from Table A the same as 



17 
Table B. 

Always name the factors taken from Table B the same as the name of declination. 



Declination. 


2 HOURS. 


3Hr. 


ra. 
00 


m. 
4 


m. 
8 


m. 
12 


m. 
16 


m. 
20 


m. 

24 


m. 
28 


m. 
32 


m. 

36 


m. 
40 


m. 
44 


rn. 
48 


m. 

52 


m. 
56 


m. 
00 


e 
































' 


o 


oo 


oo 


oo 


oo 


oo 


oo 


oo 


oo 


OO 


oo 


oo 


oo 


oo 


oo 


00 


oo 


i 


03 


03 


03 


03 


03 


03 


3 


03 


03 


03 


03 


03 


03 


03 


03 


02 


i 


07 


07 


07 


06 


06 


06 -06 


06 


06 


06 


05 


'5 


05 


05 


05 


05 


3 


10 


10 


10 


10 


09 


09 -09 


09 


09 


08 


08 


08 


08 


08 


08 


07 


4 


14 


14 


13 


13 


13 


12 '12 


12 


II 


II 


ii 


ri 


10 


10 


10 


10 


5 


17 


17 


17 


16 


16 


'IS 'IS 


15 


-I 4 


<J 4 


14 


13 


13 


13 


13 


12 


6 


21 


20 


20 


19 


19 


18 -18 


17 


17 


17 


16 


16 


16 


15 


15 


'IS 


7 


25 


24 


23 


23 


22 


21 '21 


2O 


20 


20 


19 


19 


18 


18 


18 


17 


8 


28 


27 


27 


26 


25 


25 -24 


23 


23 


'22 


'22 


21 


21 


21 


20 


20 


9 


32 




3 


29 


28 


28 


27 


26 


26 


25 


25 


24 


24 


23 


23 


22 


10 


'35 


"34 


'33 


32 


32 


'3 1 


30 


29 


29 


28 


27 


27 


26 


26 


25 


25 


ii 


39 


38 


'37 


36 


'35 


'34 


'33 


32 


32 


31 


30 


3 


29 


29 


28 


27 


12 


'43 


41 


40 


39 


38 


37 -36 


"35 


35 


34 


33 


32 


32 




31 


3 


13 


46 


'45 


'44 


42 


*4 r 


40 -39 


38 


37 


'37 


36 


J5 


35 


'34 


'33 


'33 


14 


50 


48 


'47 


46 


45 


'43 


42 


41 


40 


40 


'39 


38 


'37 


'37 


36 


35 


1 5 + 


54 


52 


'5 1 


'49 


48 


47 


46 


'45 


'44 


'43 


42 


'41 


40 


'39 


'39 


38 


16 


'57 


56 


*54 


'53 


'Si 


50 


'49 


48 


47 


46 


45 


'44 


43 


42 


'4 1 


'4 1 


17 


61 


59 


58 


56 


55 


'53 


52 


'SI 


50 


'49 


48 


*47 


46 


'45 


'44 


'43 


18 


65 


63 


61 


60 


58 


'57 


'55 


*54 


'53 


52 




50 


'49 


48 


'47 


46 


19 


69 


67 


65 


63 


62 


60 


'59 


'57 


56 


55 


54 


52 




50 


50 


'49 


20 


73 


71 


69 


67 


65 


63 


62 


60 


59 


58 


57 


55 


54 


53 


52 




21 


77 


75 


72 


70 


69 


67 


65 


64 


62 


61 


60 


'59 


57 


56 


'55 


'54 


22 


81 


78 


76 


74 


72 


70 


69 


67 


66 


64 


63 


62 


60 


'59 


58 


'57 


23 


85 


82 


80 


78 


76 


74 


72 


71 


69 


67 


66 


'65 


63 


62 


61 


60 


23 28' 


87 


-84 


82 


80 


78 


76 


74 


72 


71 


69 


68 


66 


65 


64 


62 


61 


2 4 


89 


86 


84 


82 


80 


78 


76 


74 


72 


71 


69 


68 


67 


65 


64 


63 


25 


93 


91 


88 


86 


83 


81 


79 


77 


76 


74 


73 


71 


70 


68 


67 


66 


26 


98 


95 


92 


90 


87 


85 


83 


81 


79 


78 


76 


74 


73 


72 


70 


69 


2 7 


i -02 


99 


96 


'94 


91 


89 


87 


85 


83 


81 


79 


78 


76 


75 


73 


72 


28 


i -06 


1-03 


I'OO 


98 


95 


'93 


90 


88 


86 


'84 


83 


81 


79 


78 


77 


75 


29 


I'll 


i -08 


1-05 


I'O2 


99 


'97 


'94 


92 


90 


88 


86 


84 


83 


81 


80 


78 


30 


i'i5 


1-12 


1-09 


ro6 


1-03 


I'OI 


98 


96 


94 


92 


90 


88 


86 


85 


'83 


82 


Stars. 


































N. Decln. 


































Procyon 


19 


19 


18 


18 


17 


17 


16 


16 


16 


15 


15 


15 


' T 4 


I4 


14 


'M 


Altair .. 




30 


29 


28 


27 


26 


26 


25 


25 


24 


24 


23 


23 


22 


22 


21 


Aldebar'n 


'59 


57 


'55 


54 


52 


'Si 


50 


49 


48 


'47 


4 6 


'45 


"44 


'43 


42 


4! 


Arcturus 


71 


69 


67 


66 


64 


62 


61 


59 


58 


'57 


56 


'54 


53 


52 


'SI 


51 


Castor . . 


1-25 


I'22 


1-18 


1-15 


I-I2 


1-09 


1-07 


1-04 


1-02 


1*00 


98 


96 


94 


'92 


'90 


89 


Vega .. 


i -60 


1-56 


1-51 


1-47 


i '43 


1-40 


1-36 


i'33 


I- 3 


1-27 


1-25 


I'22 


20 


17 


I'I5 


1-13 


Deneb . . 


2'OO 


1-94 


1-88 


1-83 


179 


174 


170 


1-66 


1-62 






I'52 


'49 


46 


1-44 


1-41 


Capella 


2'06 


2'OO 


i '95 


1-90 


1-85 


i -80 


176 


172 


1-68 


1-64 


1-61 


i'57 


54 


'SI 


1-49 


1-46 


a Persei . . 


2'35 


2'28 


2-21 


2-15 


2'IO 


2-04 


1-99 


i'95 


1-90 


1-86 


1-82 


179 


75 


72 


1-69 


1-66 


^UrsaeMaj. 


2- 3 6 


2-29 


2-23 


2-17 


2'II 


2-06 


2-01 


1-96 


1-92 


1-88 


1-84 


i -80 


77 


73 


170 


1-67 


e UrsseMaj. 


3'02 


2-93 




277 


270 


2-63 


2'57 


2-51 


2'45 


2-40 


2'35 


2-30 


2-25 


2'2I 


2-17 


2-13 


ctUrsaeMaj. 


3-80 


3-69 


3-58 


3'49 




3-3i 


3'23 




3-09 


3-02 


2-96 


2-90 


2-84 


279 


273 


2-69 


5. Decln. 


































Rigel .. 


29 


28 


28 


27 


26 


25 


25 


24 


24 


23 


23 


22 


22 


21 


21 


21 


Sirius . . 


60 


58 


56 


'55 


'53 


52 




50 


48 


'47 


46 


'45 


'45 


"44 


'43 


42 


e Sagittarii 


I- 37 




1-29 


1-26 


1-23 


1-19 


1-17 


1-14 


I'll 


1-09 






I -O2 


I'OO 


99 


97 


X Scorpii 


i-5i 


I'47 


1-42 


1-39 




1-32 


1-28 


1-25 


1-23 


1-20 


1-17 


I'I5 


I-I3 


I'll 


1-09 


1-07 


y Argus . . 


2-15 


2-09 


2-03 


1-97 


I-92 


!'8 7 


1-83 


179 


175 


171 


1-67 


I-6 4 


1-61 


1-58 




1-52 


a Gruis . . 


2-17 


2'II 


2-05 


2-OO 


1-94 


1-90 


1-85 


1-81 


177 


173 


1-69 


1-66 


1-63 


i'59 


1 57 


i '54 


Canopus 


2-62 


2'54 




2-41 


2'34 


2-28 


2-23 


2-18 


2-13 


2-08 


2-04 


2'00 


1-96 


1-92 


1-89 


1-85 


y Crucis . . 


3'3 


2'95 


2-86 


279 


2-71 


2-64 


2-58 


2-52 


2-46 


2-41 


2-36 


2-31 


2-27 


2'22 


2-18 


2-15 


a Pavonis 


3-08 


2-99 


2-91 


2-83276 


2-69 


2-62 


2-56 


2-50 


2'45 


2-40 


2'35 


2'3o 


2-26 


2-22 


2-18 


Achernar 


3-16 


3-07 


2-98 


2-90 


2-83 


276 


2-69 


2-63 


2'57 


2-51 


2*46 


2-41 


2-36 


2-32 


2-28 


2-24 


ft Crucis } 
e Argus J 


3-36 


3-26 


3-I7 


3'08 


3 -00 


2-93 


2'8 5 


279 


273 


2-67 


2-61 


2-56 


2-51 


2-46 


2-42 


2'37 


ft Centauri 


3-46 


3'35 


3-26 


3-17 


3-09 


3-01 


2-94 


2-87 


2-81 


274 


2-69 


2-63 


2-58 


2'53 


2-49 


2'44 


a* Centauri 


3'53 


3'43 


3'33 


3^4 


3'l6 


3-08 


3-00 


2-93 


2-87 


2-80 


275 


2-69 


2-64 


2'59 


2'54 


2-50 


a 1 Crucis.. 




375 




3*54 


3'45 


3-36 


3-28 


3-21 




3-07 


3-00 


2-94 


2-88 


2-83 


278 


273 


a Tri. Aus. 


5-I7 




4-88 


475 


4-63 




4-40 


4-30 


4-2o| 4 -n 


4-02 


3'94 


3-87 


379 


372 


3-66 


ft Argus . . 




5-i5 


5-01 


4-87 


474 


4-63 


4'5i 


4-41 




4'i3 


4-04 


3-96 


3*89 


3-82 


375 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




00 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


oo 




10 Hr. 


9 HOURS. 



2 - Azimuth. 



18 
Table A. 

When hour angle is less than 6 hours, name the factors taken from Table A contrary to name of lat. 





3 HOURS. 


4Hr. 


Lat. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




00 


4 


8 


12 


16 


20 


24 


28 


32 


86 


40 


44 


48 


52 


56 


00 


o 


. 1 t 

































* 1 * 

ool -oo 


oo 


oo 


'OO 


oo 


oo 


oo 


OO 


oo 


oo 


oo 


00 


00 


oo 


oo 


I 


02! -02 


O2 


02 


02 


01 


01 


01 


01 


01 


01 


01 


01 


01 


01 


01 


2 


03 -03 


03 


03 


03 


03 


03 


03 


03 


03 


O2 


02 


O2 


02 


C2 


02 


3 


05 


05 


5 


"5 


05 


04 


04 


04 


04 


04 


4 


04 


03 


03 


03 


'03 


4 


07 


07 


07 


06 


06 


06 


06 


05 


05 


05 


05 


05 


'05 


04 


04 


04 


5 


09 


08 


08 


08 


08 


07 


07 


07 


07 


06 


06 


06 


06 


05 


-05 


05 


6 


II 


10 


10 


09 


09 


09 


09 


08 


08 


08 


07 


07 


07 


07 


06 


06 


7 


12 


12 


II 


ii 


II 


10 


10 


10 


09 


09 


09 


08 


08 


08 


07 


07 


8 


M 


' J 4 


13 


13! -12 


12 


II 


II 


II 


10 


10 


09 


09 


09 


08 


08 


9 


16 


15 


15 


'?4 


14 


13 


13 


12 


12 


12 


II 


11 


io 


10 


io 


09 


10 


18 


17 


16 


16 


15 


15 


14 


14 


'IS 


13 


'12 


*I2 


II 


'II 


II 


10 


ii 


19 


19 


18 


18 


17 


16 


16 


15 


'IS 


M 


14 


13 


13 


'12 


'12 


II 


12 


"21 


21 


20 


19 


18 


18 


17 


17 


16 


'15 


'IS 


14 


14 


13 


13 


12 


J 3 


23 


22 


22 


21 


20 


19 


19 


18 


17 


17 


16 


16 


15 


-I 4 


'M 


13 


M 


25 


24 


23 


'22 


'22 


'21 


20 


19 


19 


18 


17 


17 


16 


16 


15 


T4 


15 


27 


26 


'25 


2 4 


23 


'22 


22 


21 


20 


19 


19 


18 


-1 7 


17 


16 


'IS 


16 


29 


28 


27 


26 


25 


2 4 


'23 


22 


22 


21 


20 


19 


19 


18 


17 


17 


17 


31 


3 


29 


28 


27 


'26 


2 5 


24 


23 


'22 


21 


21 


20 


19 


18 


18 


18 


.32 


31 


'SO 


29 


'28 


27 


26 


>2 5 


24 


24 


23 


22 


21 


20 


20 


19 


19 


'34 


33 


3 2 


31 


3 


29 


28 


27 


26 


25 


2 4 


2 3 


'22 


22 


21 


20 


20 


36 


35 


*34 


'33 


32 


'SI 


29 


28 


27 


26 


25 


25 


'24 


23 


'22 


'21 


21 


38 


37 


36 


'35 


'33 


32 


31 


30 


29 


28 


27 


26 


"25 


24 


23 


22 


22 


40 


'39 


38 


36 


'35 


'34 


'33 


32 


3 


29 


28 


27 


26 


25 


24 


23 


23 


42 


41 


40 


38 


37 


36 


'34 


33 


32 


'SI 


3 


29 


28 


27 


25 


25 


24 


*45 


'43 


42 


40 


'39 


'37 


36 


35 


'34 


32 


31 


3 


29 


28 


27 


26 


25 


'47 


'45 


43 


42 


4* 


'39 


38 


36 


35 


'34 


'33 


'SI 


3 


29 


28 


27 


26 


'49 


'47 


45 


'44 


4 2 


MI 


'39 


38 


'37 


'35 


'34 


'33 


32 


3 


29 


28 


27 


51 


'49 


48 


46 


'44 


'43 


'4 1 


40 


3 8 


'37 


36 


'34 


"33 


32 


'SI 


29 


28 


'53 


5i 


50 


48 


'46 


'45 


'43 


42 


40 


'39 


'37 


36 


'35 


'33 


32 


31 


29 


55 


'54 


52 


50 


48 


*47 


'45 


43 


42 


40 


'39 


'37 


36 


'35 


33 


32 


30 


58 


56 


54 


52 


50 


48 


"47 


45 


'44 


42 


4 


'39 


'37 


36 


35 


'33 


3 1 


60 


58 


56 


*54 


52 


'SO 


49 


47 


'45 


'44 


4 2 


41 


'39 


3 8 


36 


'35 


32 


62 


60 


58 


56 


'54 


"52 


'Si 


49 


'47 


'45 


44 


4 2 


'41 


'39 


38 


36 


33 


65 


63 


61 


58 


56 


'54 


"53 


51 


49 


'47 


"45 


'44 


42 


41 


'39 


'37 


34 


67 


65 


'63 


61 


'59 


'57 


55 


53 


51 


'49 


'47 


'45 


'44 


4 2 


41 


'39 


35 


70 


68 


65 


63 


61 


59 


'57 


55 


53 


'SI 


'49 


'47 


'45 


'44 


'42 


40 


36 


73 


70 


68 


65 


63 


61 


'59 


'57 


'55 


'53 


'Si 


'49 


'47 


45 


'44 


'42 


37 


75 


73 


70 


68 


66 


'63 


61 


"59 


57 


'55 


'53 


'Si 


'49 


'47 


'45 


'44 


38 


78 


75 


'73 


70 


68 


66 


63 


61 


59 


'57 


"55 


*53 


51 


'49 


'47 


45 


39 


81 


78 


75 


73 


70 


68 


66 


63 


61 


'59 


'57 


'55 


"53 


'SI 


'49 


'47 


40 


8 4 


81 


78 


76 


73 


70 


68 


66 


63 


61 


'59 


'57 


'54 


52 


50 


48 


41 


87 


84 


81 


78 


76 


73 


70 


68 


65 


63 


61 


'59 


56 


'54 


52 


'SO 


4 2 


90 


8? 


84 


81 


78 


76 


73 


70 


68 


65 


63 


61 


58 


56 


'54 


52 


43 


93 


90 


87 


8 4 


81 


78 


76 


73 


70 


68 


65 


63 


61 


58 


56 


54 


44 


97 


'93 


90 


87 


84 


81 


78 


75 


73 


7 


68 


65 


63 


60 


58 


56 


45 


I'OO 


'97 


93 


90 


87 


84 


81 


78 


75 


73 


70 


67 


'65 


62 


60 


58 


46 


1*04 


I'OO 


'97 


'93 


90 


87 


84 


81 


78 


75 


73 


70 


67 


65 


62 


60 


47 


1-07 


i -04 


I OO 


'97 


*93 


90 


87 


84 


81 


78 


75 


72 


70 


67 


64 


62 


48 


i'ii 


"7 


i '04 


I'OO 


97 


'93 


90 


87 


84 


81 


78 


75 


72 


69 


67 


64 


49 


ri'5 


ii 


1-07 


1-04 


I'OO 


'97 


'93 


90 


87 


84 


80 


78 


75 


72 


69 


66 


50 


rig 


15 


I'll 


1-07 


i 04 


I'OO 


'97 


'93 


90 


87 


83 


80 


77 


74 


72 


69 


51 


1*23 


ig 


i'i5 


I'll 


i 07 


'4 


oo 


96 


93 


90 


86 


83 


80 


/7*T 

// 


74 


71 


52 


1-28 


"2i 


1'IC 


1-15 


i'ii 


07 


04 


I'OO 


96 


'93 


90 


86 


83 


80 


77 


74 


53 


i'33 


28 


I'2^ 


rig 


i-i5 


ii 


07 


i 04 


roo 


96 


93 


90 


86 


83 


80 


77 


54 


1-38 


'33 


I'28 


i 24 


1-20 


15 


ii 


i 08 


I O^ 


oo 


96 


93 


89 


86 


83 


79 


55 


i'43 


38 


I'33 


1*29 


1-24 


20 


16 


I'I2 


i -08 


04 


I'OO 


96 


'93 


89 


86 


82 


56 


1-48 


'43 


I- 3 8 


i'33 


I 29 


~'2i 


2C 


i'i6 


1*12 


08 


04 


oc 


96 


93 


89 


86 


57 


i'54 


'49 


1-44 


i'39 


I'34 


2C 


25 


I'20 


1-16 


*I2 


08 


04 


I'OO 


96 


'93 


89 


58 


i -60 


55 


1'49 


1-44 


i'39 


'34 


3 c 


1-25 


1*21 


16 


'12 


08 


i -04 


I'OO 


96 


92 


59 


1-66 


61 


i'55 


1-50 


i'45 


40 


'35 


1-30 


I'25 


'21 


17 


ria 


i -08 


1-04 


I'OO 


96 


60 


173 


67 


1-62 


156 


i'5i 


1'45 


i'4C 


i'35 


I-3I 


26 


21 


17 


I'I2 


ro8 


1-04 


I '00 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 


52 


48 


44 


40 


36 


3 2 


28 


24 


20 


16 


12 


8 


4 


oo 




qTTf. 


R HOURS. 



When hour angle is more than 6 
name of the latitude. 



hours, name the factors taken from Table A the same as the 



19 
Table B. 

Always name the factors taken from Table B the same as the name of declination. 





3 HOUttS. 


4 Hr. 


TJ 1' t' n 






























UtiCi IlUfU U . 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. m. 


m. 


m. m. 


m. 


m. 


m. 


TO. 




00 


4 


8 12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 








1 























































o 


OO 


oo 


oo 


oo 


oo 


oo 


ooj -oo| -oo 


oo 


oo 


oo 


oo 


oo 


oo 


oo 


T 


O2 


02 


02 


02 


02 


02, -02 


02 


O2 


O2 


02 


02 


02 


O2 


02 


02 


2 


05 


05! '05 


05 


05 


05 -04 


04 


"4 


0-4 


04 


CM 


04 


04 


04 


04 


3 


07 


07 


07 


07 


07 


07 -07 


07 


07 


06 


06 


06 


06 


06 


06 


06 


4 


10 


10 


10 


09 


09 


09; -09 


09 


09 


09 


09 


oS 


08 


08 


08 


08 


5 


12 


12 


12 


12 


12 


II 


II 


II 


ii 


11 


ii 


II 


~*0 


10 


'"O 


10 


6 


15 


'IS 


14 


14 


14 


14 


14 


13 


13 


13 


13 


13 


' T 3 


12; -12 


12 


7 


17 


17 


17 


17 


16 


16 -16 


16 


15 


15 


15 


15 


15 


*4 


' J 4 




8 


2O 


20 




19 


19 


T -18 


18 


18 


17 


17 


17 


17 


17 


16 


16 


9 


22 


22 


22 


21 


21 


21 


20 


20 


20 


20 


19 


19 


19 


19 


18 


18 


10 


25 


25 


24 


24 


23 


23 


23 


22 


22 


22 


22 


21 


21 


21 


21 


20 


ii 


27 


27 


27 


26 


26 


25! '25 


25 


2 4 


24 


24 


23 


23 


23 


23 


22 


12 


3 


3 


2Q 


29 


28 


28 -27 


27 


27 


26 


26 


26 


25 


25 


25 


25 


13 


'33 


32 


3 2 


'SI 


"3 1 


30 -30 


29 


29 


29 


28 


28 


28 


27 


27 


27 


14 


'35 


35 


'34 


34 


33 


'33 ! -32 '32 


"3 1 


"SI 


3 


30 


3 


29 


29 


29 


15 


38 


37 


37 


36 


36 


'35 


34 


34 


*34 


33 


33 


32 


32 


32 






16 


'4 1 


40 


'39 


'39 


38 


37 


"37 


36 


36 


*35 


35 


35 


'34 


34 


*33 


'33 


17 


'43 


'43 


42 


41 


41 


4 o 


39 


39 


38 


38 


'37 


37 


36 


36 


36 


'35 


18 


46 


45 


'44 


'44 


43 


42 


42 


41 


'4 1 


40 


40 


39 


'39 


38 


38 


38 


19 


49 


48 


'47 


46 


46 


'45 


44 


'44 


*43 


'43 


42 -42 


'4 1 


'4 1 


4 


4 


20 


'5 1 


'5 1 


50 


'49 


48 


48 -47 


46 


46 


45 


'44 


'44 


'43 


"43 


42 


42 


21 


54 


53 


52 


52 


51 


50 '49 


49 


48 


47 


'47 


46 


46 


'45 


'45 


'44 


22 


57 


56 


55 


54 


54 


53! '52 




'Si 


50 


49 


'49 


48 


48 


'47 


47 


23 


60 


59 


58 


'57 


56 


'551 -55 


'54 


'53 


52 


52 


'5 1 




50 


'SO 


'49 


23 28' 


61 


60 


59 


58 


58 


'57! '56 


'55 


"54 


'54 


"53 


52 


52 


51 






24 


63 


62 


61 


60 


59 


58 


57 


57 


56 


55 


'54 


54 


53 


53 


52 


'SI 


25 


66 


65 


64 


63 


62 


61 


60 


'59 


58 


58 


57 


56 


56 


'55 


'54 


"54 


26 


69 


68 


67 


66 


65 


64 


63 


62 


61 


60 


60 


59 


58 


58 


'57 


56 


27 


72 


71 


70 


69 


68 


67 


66 


65 


64 -63 


62 


61 


61 


60 


'59 


'59 


28 


75 


74 


73 


72 


70 


69 


68 


67 


67 


66 


65 


64 


63 


63 


62 


61 


29 


78 


77 


76 


75 


73 


72 


71 


70 


69 


69 


68 


67 


66 


65 


65 


6 4 


30 


82 


80 


79 


78 


76 


75 


74 


73 


72 


71 


70 


70 


69 


68 


6 7 


67 


Stars. 


































Procyon 


14 


13 


13 


13 


13 


12 


12 


12 


12 


12 


12 


12 


ii 


ii 


II 


ii 


Altair .. 


21 


21 


21 


20 


20 


20 


2O 


19 


19 


19 


19 


18 


18 


18 


18 


18 


Aldebar'n 


41 


41 


4 


'39 


39 


38 


38 


'37 


37 


36 


36 


'35 


'35 


35 


'34 


'34 


Arcturus 


'SI 


'SO 


"49 


48 


'47 


'47 


46 


45 


'45 


'44 


'44 


'43 


'43 


42 


42 


41 


Castor . . 


8 9 


8 7 


86 


84 


'S3 


82 


81 


80 


79 


77 


77 


76 


75 


74 


73 


72 


Vega .. 


I-I 3 


I'll 


10 


i -08 


I -06 


05 


03 


I -O2 


I -00 


'99 


98 


97 


96 


94 


93 


93 


Deneb . . 


I' 4 I 


1-39 


'37 


i "34 


I-32 


30 


28 


1-27 


1-25 


1-23 


22 


20 


19 


18 


1-16 




Capella 


I- 4 6 




41 


i'39 


1-37 


35 


33 


I-3I 


1-29 


1-28 


26 


'25 


23 


22 


i -20 


1-19 


a Persei . . 


1-66 


1-63 


60 


1-58 


i'55 


53 


51 


I'49 


1-47 


J '45 


'43 


'4 1 


40 


38 


i- 37 


i '35 


jjUrsseMaj. 


1-67 


1-64 


62 


i '59 


i "57 


'54 


52 


I- 5 


1-48 


1-46 


'44 


43 


41 


39 


1-38 


1-36 


eUrsasMaj. 


2-13 


2-10 


2-06 


2-03 


2'OO 


97 


94 


I-9I 


1-89 


1-86 


84 


82 


80 


78 


176 


1-74 


aUrsseMaj. 


2-69 


2-6 4 


2'6o 


2-56 


2-52 


2-48 


2-44 


2-41 


2-38 


2'35 


2-32 


2-29 


2-27 


2-24 


2-22 


2-19 


S. Decln. 
































Rigel .. 


21 


2O 


20 


20 


19 


19 


19 


19 


18 


18 


18 


18 


17 


17 


17 


17 


Sirius .. 


H2 


41 


'4 1 


4 


39 


39 


38 


3 8 


37 


'37 


36 


36 


36 


35 


'35 


34 


e Sagittarii 


'97 


'95 


94 


92 


91 


89 


88 


87 


86 


85 


84 


83 


82 


81 


80 


79 


X Scorpii 


1-07 


I'0 5 


1-03 


1-02 


I'OO 


'99 


'97 


9 6 


'94 


93 


92 


91 


90 


89 


88 


87 


7 Argus . . 


I-52 




1-47 


1*45 


1-42 


1-40 


1-38 


1-36 


1-35 


i'33 


1-31 


1-30 


1-28 


1-27 


1-25 


1-24 


a Gruis . . 


J '54 


1*51 


1-49 


1-46 


1-44 


1-42 


i '40 


1-38 


1-36 


i'34 


i'33 


1-31 


1-30 


1-28 


1-27 


1-26 


Canopus 


1-85 


1-82 


179 


176 


174 


171 


1-69 


i-66| 1-64 


1-62 


i -60 


1-58 


1-56 


I "54 


i'53 


1*51 


7 Crucis . . 


2-15 


2-II 


2-07 


2'O4 


2'O1 


1-98 


i'95 


i '93 


1-901-88 


1-85 


1-83 


1-81 


179 


1-77 




a Pavonis 


2*1 8 


2-14 


2-II 


2-07 


2-04 


2-01 


1-98 


1-96 


i'93 


1-91 


1-88 


1-86 


1-84 


1-82 


i -80 


III 


Achernar 


2-24 


2'2O 


2-16 


2U3 


2'10 


2'06 


2-03 


2-01 


1-98 




i'93 


1-91 


1-89 


1-86 


1-84 


1-83 


3 Crucis ) 


































e Argus [ 


2'37 


2'33 


2-29 


2'26 


2-22 


2-I 9 


2-16 


2-13 


2-10 


2-07 


2-05 


2'O2 


2-00 


1-98 


1-96 


1-94 


/3 Centauri 


2'44 


2-40 


2- 3 6 


2-32 


2-29 


2-26 


2'22 


2-I 9 


2-16 


2-14 


2'II 


2'08 


2-06 


2-04 


2'02 


2-00 


a' 2 Centauri 


2-50 


2'45 


2-41 


2'37 


2-34 


2-30 


2-27 


2-24 


2'2I 


2-18 


2-I5 


2'13 


2'10 


2-08 


2'06 


2'0 4 


a 1 Crucis . . 


273 


2-68 


2-64 


2'6o 


2-56 




2-48 


2'45 


2-42 


2-38 


2- 3 6 


2'33 


2-30 


2-27 


2-25 


2-23 


a Tri. Aus. 


3-66 


3-60 


3-54 


3-48 


3'43 


3;38 


3'33 


3-28 


3-24 


Q*2O 




3*12 3-08 


3*05 


3 -02 


2 -99 


/8 Argus .. 


375 


3-69 


3^3 


3-57 


3'52 






3'37 


3-32 


3-28 


3'24 


3-20! 3-16 


3-13 


3-10 


3-06 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


oo 




9Hr. 


8 HOURS. 



Table A. 

When hour angle is less than 6 hours, name the factors taken from Table A contrary to name of lat. 





4 HOURS. 


5Hr. 


"3 

k_3 


m. 


rn. 


m. 


m. 


m. 


ru. m. m. 


m. 


m. 


m. 


m. 


in. 


m. 


m. 


m. 




00 


4 


8 


12 16 


20 24 28 


32 


36 


40 


44 


48 


52 


56 


00 








































ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


I 


oio 


oio 


009 


009 


009 


008 


008 


007 


007 


007 


006 


006 


006 


005 


005 


005 


2 


02O 


019 


019 


018 


017 


016 


016 


015 


014 


013 


013 


'OI2 


on 


on 


oio 


009 


3 


030 


029 


028 


027 


026 


024 


023 


O22 


021 


O2O 


019 


018 


017 


016 


015 


014 


4 


040 


039 


037 


036 


034 


033 


031 


030 


028 


027 


025 


024 


023 


O2I 


O2O 


019 


5 


051 


048 


047 


045 


43 


4 I 


039 


037 


035 


034 


032 


030 


028 


027 


025 


023 


6 


061 


058 


056 


054 


051 


049 


047 


045 


4 2 


040 


038 


036 


034 


032 


030 


028 


7 


071 


068 


065 


063 


060 


057 


055 


052 


050 


047 


045 


042 


040 


038 


035 


033 


8 


081 


078 


075 


072 


069 


066 


063 


060 


057 


054 


051 


048 


046 


043 


040 


038 


9 


091 


088 


084 


081 


077 


074 


071 


06 7 


064 


061 


058 


055 


051 


048 


'045 


042 


to 


102 


098 


094 


090 


086 


082 


079 


075 


071 


068 


064 


061 


057 


054 


051 


047 


ii 


112 


108 


103 


099 


095 


091 


087 


08 3 


079 


075 


071 


067 


063 


059 


056 


052 


12 


123 


118 


113 


108 


104 


099 


095 


090 


086 


082 


077 


073 


069 


065 


061 


057 


13 


133 


128 


123 


118 


113 


108 


103 


098 


093 


089 


084 


079 


075 


071 


066 


062 


14 


144 


138 


133 


127 


122 


116 


in 


106 


101 


096 


091 


086 


081 


076 


071 


067 


15 


155 


149 


142 


137 


I 3 I 


125 


119 


114 


108 


103 


098 


092 


087 


082 


077 


072 


16 


166 


159 


152 


146 


I 4 


134 


128 


122 


116 


no 


104 


099 


093 


088 


082 


077 


17 


177 


169 


163 


156 


149 


143 


136 


130 


124 


117 


in 


105 


099 


093 


088 


082 


18 


188 


180 


173 


166 


158 


152 


'MS 


138 


131 


125 


118 


*II2 


106 


099 


093 


087 


19 


199 


191 


183 


175 


168 


161 


153 


I 4 6 


139 


132 


125 


119 


*II2 


105 


099 


092 


20 


'2IO 


202 


194 


185 


178 


170 


162 


'!54 


147 


140 


132 


125 


118 


III 


104 


098 


21 


222 


213 


204 


196 


187 


179 


171 


163 


155 


147 


140 


132 


125 


117 


no 


103 


22 


233 


224 


215 


206 


197 


188 


180 


171 


163 


155 


147 


139 


131 


124 


116 


108 


23 


245 


235 


226 


216 


207 


198 


189 


180 


171 


163 


J 54 


I 4 6 


138 


130 


*I22 


114 


24 


257 


247 


237 


227 


217 


208 


198 


189 


180 


171 


162 


153 


^45 


136 


128 


119 


25 


26 9 


258 


248 


238 


227 


217 


208 


198 


188 


179 


170 


161 


152 


143 


134 


125 


26 


282 


270 


259 


249 


238 


227 


217 


207 


197 


187 


178 


168 


158 


149 


I 4 


131 


27 


294 


282 


271 


260 


249 


238 


227 


216 


206 


196 


185 


175 


166 


156 


I 4 6 


i37 


28 


307 


295 


283 


271 


259 


248 


237 


226 


215 


204 


194 


183 


173 


163 


152 


142 


29 


3 20 


307 


295 


282 


270 


258 


247 


235 


224 


213 


202 


191 


180 


169 


159 


149 


3 


'333 


320 


307 


294 


282 


269 


257 


245 


233 


222 


'2IO 


199 


188 


177 


166 


155 


3 1 


'347 


'333 


319 


306 


293 


280 


268 


255 


243 


231 


219 


207 


195 


184 


172 


161 


32 


361 


346 


332 


3i8 


305 


291 


278 


265 


252 


2 4 


227 


215 


203 


191 


179 


167 


33 


'375 


360 


'345 


331 


317 


303 


289 


276 


262 


'249 


2 3 6 


224 


211 


199 


186 


174 


34 


389 


'374 


'359 


'344 


329 


315 


300 


286 


273 


259 


2 4 6 


232 


219 


206 


193 


181 


35 


404 


388 


372 


'357 


342 


327 


312 


297 


283 


269 


'255 


241 


228 


214 


2OI 


188 


36 


419 


403 


386 


370 


'354 


'339 


323 


308 


294 


279 


264 


250 


2 3 6 


*222 


208 


195 


37 


'435 


418 


401 


384 


368 


35i 


336 


320 


304 


289 


274 


259 


245 


230 


216 


202 


38 


45i 


'433 


415 


398 


381 


364 


348 


332 


316 


300 


28 4 


269 


254 


239 


224 


209 


39 


468 


'449 


43i 


HI3 


"395 


378 


361 


'344 


327 


3 II 


295 


279 


263 


2 4 8 


232 


217 


40 


484 


465 


446 


428 


409 


39i 


"374 


356 


'339 


322 


305 


289 


273 


257 


241 


225 


4i 


502 


482 


462 


'443 


424 


M05 


387 


369 


351 


'334 


3 l6 


299 


282 


266 


249 


233 


42 


520 


'499 


'479 


'459 


"439 


420 


401 


382 


'364 


346 


328 


310 


293 


275 


258 


241 


43 


538 


517 


496 


"475 


'455 


'435 


415 


396 


'377 


35 8 


'339 


321 


303 


285 


267 


250 


44 


558 


'535 


513 


492 


47i 


450 


430 


410 


390 


371 


'351 


'333 


3*4 


295 


277 


259 


45 


'577 


'554 


532 


510 


488 


466 


*445 


424 


404 


384 


364 


'344 


325 


3 06 


287 


268 


46 


598 


'574 


55i 


528 


505 


483 


461 


440 


418 


398 


'377 


'357 


336 


317 


297 


277 


47 


619 


'594 


570 


546 


523 


500 


'477 


'455 


'433 


412 


390 


369 


348 


328 


307 


287 


48 


641 


616 


59i 


566 


542 


518 


'494 


471 


'449 


4 26 


404 


382 


3 6l 


340 


318 


298 


49 


664 


638 


612 


586 


561 


536 


512 


488 


465 


44 2 


419 


396 


'374 


352 


330 


308 


50 


688 


661 


* 6 34 


607 


58i 


556 


53i 


506 


481 


'457 


'434 


410 


387 


364 


342 


3 J 9 


51 


713 


685 


657 


629 


602 


576 


550 


524 


'499 


'474 


'449 


425 


4 OI 


378 


354 


33i 


52 


'739 


709 


681 


652 


624 


'597 


'57 


'543 


517 


491 


466 


441 


416 


391 


367 


'343 


53 


766 


736 


706 


676 


647 


619 


59i 


563 


536 


509 


483 


'457 


431 


406 


381 


356 


54 


'795 


763 


732 


701 


671 


642 


613 


584 


556 


528 


501 


'474 


'447 


4 2I 


395 


369 


55 


825 


792 


'759 


728 


697 


666 


636 


606 


577 


548 


520 


492 


464 


'437 


410 


383 


56 


856 


822 


788 


755 


723 


691 


660 


629 


'599 


'569 


540 


510 


482 


'453 


425 


'397 


57 


889 


854 


819 


785 


75i 


718 


686 


654 


622 


591 


560 


530 


500 


471 


442 


'413 


58 


924 


887 


851 


815 


781 


746 


713 


679 


647 


'614 


582 


55i 


520 


489 


459 


429 


59 


961 


923 


885 


848 


812 


776 


741 


706 


672 


6^9 


606 


"573 


541 


509 


477 


446 


60 


ooo 


960 


921 


883 


845 


808 


771 


'735 


700 


665 


630 


596 


563 


530 


497 


464 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 


52 


48 


44 


40 


36 


32 


28 24 


20 


16 


12 


8 


4 


o 




8Hr. 


7 HOURS. 



When hour angle is more than 6 hours, 
name of the latitude. 



name the factors taken from Table A the same as the 



" 



21 
Table B. 

Always name the factors taken from Table B the same 



the name of declination. 





4 HOURS. 


5 Hr. 


Declination. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




00 


-i 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


58 


00 


o 


































O 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


I 


O20 


020 


020 


'O2O 


019 


019 


019 


019 


019 


019 


019 


018 


018 


018 


018 


018 


2 


"040 


040 


040 


039 


039 


039 


038 


038 


038 


037 


'037 


037 


037 


'037 


036 


036 


3 


061 


060 


059 


059 


058 


058 


057 


057 


057 


056 


056 


055 


055 


055 


055 


054 


4 


081 


080 


079 


078 


078 


077 


077 


076 


075 


075 


074 


074 


074 


073 


073 


072 


5 


101 


100 


099 


098 


097 


097 


096 


095 


094 


094 


093 


093 


092 


091 


091 


091 


6 


121 


'120 


119 


118 


117 


116 


115 


114 


113 


113 


112 


III 


in 


no 


109 


109 


7 


I 4 2 


I 4 


139 


138 


137 


135 


'134 


133 


132 


132 


131 


130 


129 


128 


128 


127 


8 


162 


161 


159 


158 


156 


'155 


'154 


153 


152 


151 


150 


149 


148 


147 


146 


145 


9 


'183 


181 


179 


178 


176 


' J 75 


173 


172 


171 


170 


I6 9 


168 


167 


166 


165 


l6a 


10 


20 4 


202 


200 


198 


196 


195 


193 


192 


190 


189 


188 


186 


185 


184 


183 


183 


ii 


224 


222 


'220 


218 


216 


214 


213 


211 


210 


208 


207 


206 


204 


203 


202 


2OI 


12 


245 


243 


241 


'239 


236 


'235 


'233 


2 3 I 


229 


228 


226 


225 


223 


222 


'221 


220 


JT 


267 


264 


26l 


'259 


257 


255 


253 


251 


2 4 9 


247 


246 


244 


243 


"241 


240 


239 


14 


288 


285 


282 


280 


277 


275 


273 


271 


269 


267 


265 


264 


262 


26l 


'259 




15 


309 


3 06 


303 


301 


298 


296 


'293 


291 


289 


287 


285 


283 


282 


280 


279 


'277 


16 


'33 1 


328 


325 


322 


319 


316 


314 


3 I2 


309 


307 


305 


303 


302 


3 00 


2 9 8 


'297 


17 


'353 


350 


346 


'343 


340 


'337 


'335 


332 


'33 


327 


325 


323 


321 


3 20 


318 


317 


18 


'375 


'37 1 


368 


365 


362 


'359 


356 


'353 


'350 


348 


346 


'344 


'342 


340 


338 


326 


19 


398 


'394 


390 


386 


383 


380 


'377 


'374 


371 


369 


366 


364 


362 


3 60 


358 




20 


420 


416 


412 


408 


405 


402 


398 


395 


'393 


390 


387 


385 


383 


381 


'379 


'377 


21 


'443 


'439 


'435 


431 


427 


424 


420 


417 


414 


411 


408 


406 


404 


4 OI 


'399 


'397 


22 


467 


462 


45 S 


'453 


450 


446 


'442 


'439 


436 


433 


430 


427 


425 


4 22 


4 20 


4 I8 


23 


490 


'485 


4 8l 


476 


472 


468 


465 


461 


458 


455 


'452 


'449 


446 


'444 


442 


'439 


2 3 28' 


501 


496 


'492 


487 


483 


'479 


'475 


472 


468 


465 


462 


'459 


456 


'454 


452 


'449 


24 


514 


509 


504 


500 


495 


491 


487 


484 


4 80 


477 


'474 


471 


468 


466 


M63 


4 6l 


25 


538 


'533 


528 


'523 


519 


'SIS 


510 


507 


503 


499 


496 


'493 


490 


488 


485 


483 


26 


563 


558 


552 


'547 


543 


538 


'534 


'530 


526 


522 


519 


516 


513 


510 


507 


'SOS 


27 


588 


583 


'577 


572 


567 


562 


558 


'554 


'550 


546 


542 


'539 


536 


'533 


'530 


527 


28 


614 


608 


602 


'597 


592 


587 


582 


578 


'573 


57 


566 


562 


'559 


'556 


'553 


'550 


29 


640 


634 


628 


622 


617 


612 


607 


602 


598 


'594 


590 


586 


583 


580 


'577 


'574 




667 


660 


654 


648 


642 


'637 


'632 


627 


623 


618 


614 


611 


607 


60 4 


601 


598 


Stars. 


































N. Decln. 


































Procyon 


no 


109 


108 


107 


106 


105 


105 


104 


103 


IO2 


102 


101 


100 


100 


099 


090 


Altair .. 


175 




172 


170 


169 


167 


166 


165 


I6 4 


163 


161 


160 


160 


159 


158 


'157 


Aldebar'n 


338 


'335 


'332 


329 


326 


323 


321 


318 


316 


314 


312 


310 


308 


3 06 


'35 


303 


Arcturus 


412 


408 


'405 


401 


'397 


'394 


'391 


388 


385 


383 


380 


378 


376 


'373 


37 2 


37 


Castor . . 


724 


717 


710 


704 


698 


692 


686 


681 


676 


672 


667 


663 


659 


656 


652 


649 


Vega .. 


'925 


916 


907 


899 


891 


884 


877 


870 


864 


8 5 8 


852 


847 


842 


8 3 8 


833 


829 


Deneb . . 


1-15 


1-14 


"13 


1*12 


ii 


no 


1-09 


08 


I -08 


1-07 


06 


06 


05 


I-0 4 


04 


1-03 


Capella 


1-19 


n8 


17 


n6 


'IS 


1-14 


1-13 


12 


I'll 


I'll 


no 


09 


09 


I -08 


07 


1-07 


a Persei . . 


!'35 


i- 34 


'33 


1-32 


30 


1-29 


1-28 


27 


1-26 


1-26 


1-25 


24 


23 


1-23 


'22 


I'2I 


?;UrsaeMaj 


i'36 


i '35 


'34 


i - 33 


31 


1-30 


1-29 


28 


1-27 


1-27 


1-26 


'25 


24 


I-2 4 


23 


I'22 


eUrsasMaj. 


**74 


172 


71 


1-69 


68 


r66 


1-65 


6 4 


I-6 3 


1-62 


i -60 


'59 


'59 


I-58 


'57 


I- 5 6 


a Ursae Maj 


2-19 


2-17 


2-15 


2-13 


2-II 


2"IO 


2-08 


2'06 


2-05 


2-03 


2'O2 


2'OI 


oo 


I'99 


98 


I '97 


S. Decln. 


































Rigel .. 


!6 9 


I6 7 


165 


164 


162 


161 


160 


159 


157 


I 5 6 


155 


154 


153 


153 


152 


'J5 1 


Sirius . . 


'344 


"34 1 


'337 


'334 


332 


329 


326 


324 


321 


319 


317 


315 


313 


3 II 


310 


308 


e Sagittarii 
X Scorpii 


791 
871 


784 
863 


776 
'855 


769 
847 


763 
840 


756 
833 


750 
826 


745 
820 


739 
814 


734 
808 


729 
803 


725 
798 


721 
793 


717 
789 


7*3 
785 


710 

781 


7 Argus 




1-23 


I'22 


I-2I 


f20 


1-19 


1-18 


1-17 


n6 


i' J 5 


I-I4 


I-I4 


1-13 


I'I2 


I-I2 


i-ii 


a Gruis 


1-26 


" 2 4 


I'23 


'22 


I -21 


T'20 


19 


1-18 


1-17 


16 


1-16 


1 ' 1 5 


1-14 


I-I4 


I-I3 


1-13 


Canopus 




"5 


1-48 


'47 


I' 4 6 


i'45 


'43 


1-42 


1-41 


40 


i '39 


i '39 


1-38 


i '37 


136 


1-36 


7 Crucis . . 


r '75 


73 


172 


70 


I-6 9 


1-67 


66 


1-65 


1-64 


'63 


1-61 


1-60 


i -60 


i '59 


I-58 


I- 57 


a Pavonis 


r 7 8 


76 


175 


73 


171 


1-70 


69 


1*67 


1-66 


'65 


1-64 


1-63 


1-62 


1-61 


I '60 


i -60 


Achernar 


1-83 


81 


179 


77 


176 


1-74 


73 


172 


171 


69 


1-68 


1-67 


1-66 


1-65 


1-65 


1-64 


j3 Crucis 1 
e Argus ) 


1-94 


1-92 


1-90 


1-88 


I-8 7 


1-85 


1-84 


1-82 


1-81 


i -80 


179 


177 


176 


i'75 


175 


174 


j8 Centauri 


2'OO 


1-98 


I- 9 6 


1-94 


I-92 


1-91 


1-89 


1-88 


1-86 


1-85 


1-84 


i'8 3 


1-82 


1-81 


I -80 


179 


a' 2 Centauri 


2'O4 


2'O2 


2-00 


1-98 


I- 9 6 






1-92 


i '90 


1-89 


1-88 


1-87 


1-86 


r8 5 


I-8 4 


1-83 


a 1 Crucis . . 


2-23 


2'2I 


2-18 


2-17 




2-13 


2'II 


2'IO 


2-08 


2-07 


2-05 


2-04 


2-03 


2'02 


2'OI 


2*00 


a Tri. Aus. 




2-96 


2 '93 


2*90 


2-88 


2-85 


2*83 


2'8l 


279 


2'77 


275 


274 


272 


270 


2-69 


2-68 


J3 Argus . . 


3-06 


3'3 


3-oo 


2-98 


2 '95 


2-93 


2-90 


2-88 


2-86 


2-84 


2-82 


2'8l 


279 


277 


276 


275 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




00 


56 


5- 


48 


44 


40 


36 


3 2 


28 


24 


20 


16 


12 


8 


4 


00 






7 HOURS. 



Table A. 

When hour angle is less than 6 hours, name the factors taken from Table A contrary to name of lat. 





5 HOURS. 


6Hr. 


d 


m. 


m. 


m. 


rn. 


m. 


m. 


m. m. m. 


m. 


in. 


m. 


m. 


m. 


m. 


m. 




00 


4 


8 


12 


16 


20 


M 


28 32 


38 


40 


<U 


48 


52 


56 


00 


o 


< 


, 


( 


/ 


/ 


i 


/ , 


, 


/ 


/ 


, 


, 


/ 


/ 


I 





ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo 


I 


005 


004 


004 


004 


003 


003 


003 


'O02 


002 


002 


'002 


ooi 


ooi 


ooi 


ooo 


ooo 


2 


009 


009 


008 


007 


007 


006 


006 


O05 


004 


004 


003 


002 


002 


ooi 


ooi 


ooo 


3 


014 


013 


012 


on 


oio 


009 


008 


007 


'OO6 


006 


005 


00 4 


003 


OO2 


ooi 


ooo 


4 


019 


017 


016 


015 


014 


012 


on 


oio 


009 


00 7 


006 


005 


004 


O02 


ooi 


ooo 


5 


023 


O22 


020 


019 


017 


OI 5 


014 


OI2 


on 


009 


008 


006 


00 5 


003 


'OO2 


ooo 


6 


028 


'026 


024 


022 


020 


019 


017 


015 


013 


on 


009 


007 


006 


00 4 


O02 


ooo 


7 


033 


3 I 


028 


O26 


02 4 


'O22 


019 


017 


015 


013 


on 


009 


006 


004 


002 


ooo 


8 


038 


035 


032 


030 


027 


025 


022 


020 


017 


015 


012 


oio 


007 


005 


003 


ooo 


9 


042 


039 


037 


034 


031 


028 


025 


022 


019 


017 


014 


on 


008 


006 


003 


'OOO 


10 


047 


44 


041 


037 


034 


031 


028 


025 


022 


019 


015 


OI2 


009 


006 


003 


ooo 


ii 


052 


048 


045 


4 I 


038 


034 


031 


027 


024 


O20 


017 


014 


oio 


00 7 


00 3 


ooo 


12 


057 


'053 


049 


045 


041 


037 


034 


030 


026 


'022 


019 


015 


on 


007 


004 


ooo 


13 


062 


058 


053 


049 


045 


'041 


037 


032 


028 


024 


020 


016 


OI2 


008 


OO4 


ooo 


14 


067 


062 


058 


053 


048 


44 


039 


035 


031 


026 


022 


017 


013 


009 


004 


ooo 


15 


072 


067 


062 


057 


052 


047 


042 


038 


033 


028 


023 


019 


OI 4 


009 


005 


ooo 


16 


077 


071 


066 


06 1 


056 


051 


045 


040 


035 


030 


025 


020 


015 


oio 


005 


ooo 


*7 


082 


076 


071 


06 5 


059 


054 


048 


043 


038 


032 


027 


02 1 


016 


on 


005 


ooo 


18 


087 


081 


075 


069 


06 3 


057 


051 


046 


040 


034 


028 


023 


017 


'Oil 


006 


ooo 


19 


092 


086 


079 


073 


06 7 


061 


055 


048 


042 


036 


030 


024 


018 


'012 


*oo6 


ooo 


20 


098 


091 


084 


077 


071 


064 


058 


051 


045 


038 


032 


025 


019 


013 


006 


ooo 


21 


103 


096 


089 


082 


075 


068 


061 


054 


047 


040 


034 


027 


020 


OI 3 


007 


ooo 


22 


108 


101 


093 


086 


079 


071 


064 


057 


050 


042 


035 


028 


021 


014 


007 


ooo 


23 


114 


106 


098 


090 


083 


075 


067 


060 


052 


045 


037 


030 


O22 


015 


007 


ooo 


24 


119 


in 


103 


095 


087 


079 


071 


06 3 


055 


047 


039 


031 


023 


016 


008 


ooo 


25 


125 


116 


108 


099 


091 


082 


074 


066 


057 


049 


4 I 


033 


02 4 


016 


008 


ooo 


26 


131 


122 


113 


104 


095 


086 


077 


06 9 


060 


051 


043 


034 


O26 


017 


009 


ooo 


27 


137 


127 


118 


108 


099 


090 


081 


072 


063 


054 


045 


036 


027 


018 


009 


ooo 


28 


142 


133 


123 


113 


103 


094 


084 


075 


065 


056 


047 


037 


028 


019 


009 


ooo 


29 


149 


138 


128 


118 


108 


098 


088 


078 


068 


5 8 


048 


039 


029 


019 


oio 


ooo 


30 


155 


144 


133 


123 


112 


IO2 


091 


081 


071 


061 


051 


040 


030 


020 


oio 


ooo 


31 


161 


I 5 


139 


128 


117 


106 


095 


084 


074 


063 


053 


042 


031 


021 


oio 


ooo 


32 


167 


156 


144 


133 


121 


no 


099 


088 


077 


066 


'055 


044 


033 


'022 


on 


ooo 


33 


174 


162 


150 


138 


126 


115 


103 


091 


080 


068 


057 


045 


034 


023 


on 


ooo 


34 


181 


168 


156 


143 


131 


119 


107 


095 


083 


071 


059 


047 


035 


02 4 


012 


ooo 


35 


188 


175 


162 


149 


136 


123 


in 


098 


086 


074 


061 


049 


037 


02 4 


012 


ooo 


36 


195 


181 


168 


'!54 


141 


128 


ii5 


IO2 


089 


076 


064 


051 


038 


025 


013 


ooo 


37 


202 


188 


174 


160 


J 4 6 


133 


119 


106 


093 


079 


066 


053 


039 


O26 


013 


ooo 


38 


209 


195 


180 


166 


152 


138 


124 


no 


096 


082 


068 


055 


4 I 


027 


014 


ooo 


39 


217 


'202 


187 


172 


157 


143 


128 


114 


099 


085 


071 


057 


042 


028 


014 


ooo 


40 


225 


209 


194 


178 


I6 3 


148 


133 


118 


103 


088 


073 


059 


44 


029 


015 


ooo 


4 1 


233 


217 


201 


185 


I6 9 


153 


138 


122 


107 


091 


076 


061 


046 


O3O 


015 


ooo 


42 


2 4 I 


22 4 


208 


191 


175 


159 


143 


127 


in 


095 


079 


063 


047 


031 


016 


ooo 


43 


250 


233 


215 


198 


181 


164 


148 


131 


114 


098 


082 


065 


049 


033 


016 


ooo 


44 


259 


2 4 I 


223 


205 


188 


170 


153 


136 


119 


101 


084 


068 


5 I 


034 


017 


ooo 


45 


268 


249 


231 


213 


194 


176 


'158 


I 4 I 


123 


105 


087 


070 


052 


035 


017 


ooo 


46 


277 


2 5 8 


239 


220 


*2OI 


183 


164 


1 4 6 


127 


109 


091 


072 


054 


036 


018 


ooo 


47 


287 


267 


2 4 8 


228 


208 


189 


170 


151 


132 


113 


094 


075 


056 


37 


019 


ooo 


43 


298 


277 


2 5 6 


2 3 6 


216 


196 


176 


I 5 6 


136 


117 


097 


078 


058 


039 


019 


ooo 


49 


308 


287 


266 


245 


224 


203 


182 


162 


141 


121 


101 


080 


060 


040 


Q2O 


ooo 


50 


319 


297 


275 


253 


232 


210 


189 


I6 7 


146 


125 


104 


083 


062 


042 


021 


ooo 


51 


331 


308 


285 


262 


240 


218 


196 


174 


152 


130 


108 


086 


06 5 


043 


022 


ooo 


52 


'343 


319 


295 


272 


249 


226 


203 


180 


157 


135 


112 


090 


06 7 


045 


022 


ooo 


53 


356 


331 


3 06 


282 


258 


234 


2IO 


187 


163 


139 


116 


093 


070 


'046 


023 


ooo 


54 


369 


'343 


318 


293 


268 


243 


218 


193 


169 


'MS 


I2O 


096 


072 


048 


024 


ooo 


55 


383 


356 


330 


304 


278 


252 


226 


2OI 


175 


150 


125 


100 


075 


O50 


025 


ooo 


56 


"397 


370 


342 


315 


288 


261 


235 


208 


182 


I 5 6 


I 3 


104 


078 


052 


O26 


ooo 


57 


413 


384 


356 


327 


299 


272 


244 


216 


189 


162 


135 


108 


081 


054 


027 


ooo 


58 


429 


399 


369 


340 


311 


282 


253 


225 


196 


168 


140 


112 


084 


056 


028 


'OOO 


59 


446 


415 


384 


'354 


324 


293 


264 


234 


204 


175 


I 4 6 


116 


087 


058 


O29 


ooo 


60 


464 


432 


400 


3 68 


337 


305 


274 


243 


213 


182 


152 


121 


091 


060 


030 


ooo 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. m. 


m. 


m, j m. 


m. 


m. 


m. 




00 


56 


52 


48 


44 


40 


36 


32 


28 i 24 


20 


16 \ 12 


8 


4 


00 




7 Hr. 


6 HOURS. 



When hour angle is more than 6 hours, 
Tname of the latitude. 



name the factors taken from Table A the same as the 



Table B. 
Always name the factors taken from Table B the same as the name of declination. 





5 HOURS. 


6 Hr. 


Declination. 


m. 


m. 


m. m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




00 


4 


8 12 


16 




20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 


o 




- 




























O 


ooo 


ooo 


"000 


ooo 


ooo 


ooo 


ooo 


ooo 


ooo' 'ooo 


ooo 


ooo 


ooo 


ooo 


'OOO 


ooo 


I 


018 


018 


018 


018 


018 


018 


018 


018 


018 -018 


018 


017 


017 


017 


017 


017 


2 


036 


036 


036 


036 


036 


035 


035 


035 


035 


035 


035 


035 


035 


035 


035 


035 


3 


054 


054 


054 


054 


053 


053 


053 


053 


'53 


053 


053 


053 


052 -052 


052 


052 


4 


072 


072 


072 


071 


071 


071 


071 


071 


070 


070 


070 


070 


070! '070! '070 


070 


5 


091 


090 


090 


089 


089 


089 


089 


088 


088 


088 


088 


088 


088 -088! -088 


087 


6 


109 


108 


108 


107 


107 


107 


106 


106 


106 


106 


106 


105 


iO5j '105 -105 


105 


r> 
/ 


127 


127 


126 


126 


125 


125 


124 


124 


124 


123 


123 


123 


123 -123 


123 


123 


8 


145 


-1 45 


144 


144 


143 


'M3 


142 


! 4 2 


142 


141 


141 


141 


141 -141 


141 


141 


9 


164 


163 


163 


162 


161 


161 


160 


160 


160 


159 


159 


159 


159 


158 


158 


158 


10 


183 


182 


181 


180 


180 


179 


179 


178 


178 


177 


177 


177 


177 


176 


! 7 6 


176 


ii 


201 


200 


199 


199 


198 


197 


197 


IQ 6 


196 


195 


195 


195 


195! '194 


194 


194 


12 


220 


219 


218 


217 


217 


216 


215 


215 


214 


214 


213 


213 


213 


213 


213 


213 


13 


239 


238 


237 


236 


235 


234 


234 


233 


233 


232 


232 


231 


231 


231 


231 


231 


14 


2 5 8 


257 


256 


255 


254 


253 


252 


252 


251 


251 


250 


250 


250 


249 


249 


249 


15 


277 


276 


275 


274 


273 


272 


271 


271 


270 


269 


269 


269 


268 


268 


268 


268 


16 


297 


296 


294 


293 


292 


291 


290 


290 


289 


288 


288 


287 


287 


287 


287 


287 


1 7 


317 


315 


3M 


313 


311 


310 


310 


309 


308 


307 


307 


306 


306 


306 


306 


306 


18 


336 


'335 


'333 


332 


'33' 


330 


3 2 9 


328 


327 


327 


326 


326 


325 


325 


325 


325 


19 


356 


'355 


'353 


352 


351 


350 


'349 


348 


347 


346 


346 


345 


'345 


'345 


344 


'344 


20 


'377 


'375 


'374 


37 2 


371 


370 


369 


368 


367 


366 


365 


365 


364 


364 


3&H 


364 


21 


'397 


396 


'394 


392 


39i 


390 


389 


388 


387 


386 


385 


385 


384 


384 


384 


38 4 


22 


4 l8 


416 


'4 J 5 


413 


412 


410 


409 


408 


407 


406 


406 


405 


'45 


404 


404 


404 


23 


'439 


'437 


436 


'434 


432 


43i 


430 


429 


428 


427 


426 


426 


425 


425 


425 


424 


2 3 28' 


*449 


'447 


446 


*444 


442 


441 


440 


438 


'437 


'437 


436 


435 


'435i '434 


'434 


'434 


24 


4 6! 


'459 


'457 


'455 


'454 


452 


451 


450 


'449 


448 


'447 


446 


446 


'445 


'445 


'445 


25 


483 


481 


'479 


"477 


'475 


'474 


472 


x '47i 


470 


469 


468 


467 


467 


467 


466 


466 


26 


505 


503 


501 


*499 


'497 


'495 


'494 


'493 


491 


490 


490 


489 


488 


488 


488 


488 


27 


527 


525 


523 


521 


519 


517 


516 


5i5 


513 


512 


511 


511 


510 


510 


510 


510 


28 


550 


548 


546 


'544 


542 


'54 


538 


'537 


536 


'535 


'534 


533 


532 


532 


532 


532 


29 


'574 


'57 1 


569 


567 


565 


563 


561 


560 


558 


'557 


556 


556 


555 


'555 


'554 


'554 


_3?__ 


59 8 


595 


'593 


590 


588 


586 


585 


583 


582 


581 


580 


579 


578 


578 


577 


'577 


Stars. 


































N. Decln. 


































Procyon 


099 


098 


098 


098 


097 


097 


097 


096 


096 


096 


096 


096 


096 


096 


096 


096 


Altair .. 


157 


156 


156 


155 


155 


154 


154 


153 


153 


153 


152 


152 


152 


152 


152 


152 


Aldebar'n 


303 


302 


301 


300 


298 


297 


297 


296 


295 


295 


'294 


294 


2Q3 


293 


293 


293 


Arcturus 


370 


368 


367 


365 


364 


363 


362 


361 


360 


'359 


359 


358 


358 


'357 


'357 


'357 


Castor . . 


649 


646 


643 


641 


639 


637 


635 


633 


632 


630 


629 


628 


628 


627 


62? 


627 


Vega .. 


829 


826 


822 


819 


816 


813 


811 


809 


807 


806 


804 


803 


802 


802 


801 


801 


Deneb . . 


1-03 


1-03 


I'O2 


I'O2 


I'02 


oi 


I'OI 


oi 


I'OI 


oo 


oo 


I'OO 


oo 


I'OO 


I'OO 


I -00 


Capella 


07 


i -06 


I '06 


I -06 


1-05 


1-05 


1-05 


04 


i -04 


04 


1-04 


1-03 


03 


1-03 


1-03 


1-03 


aPersei .. 


I'2I 


I'2I 


I'2O 


J'2O 


1*19 


19 


1-19 


18 


ri8 


18 


1-18 


1-17 


17 


1-17 


1-17 


1-17 


7/UrsaeMaj 


1-22 


I'22 


I'2I 


1*21 


I'20 


I'20 


I'2O 


19 


1-19 


19 


1-19 


1-18 


18 


1-18 


1-18 


1-18 


eUrsaeMaj 


1-56 


1*55 


i'55 


i'54 


i'54 


i'53 


I'53 


52 


1-52 


52 


i'5i 


i'5i 


51 


1*51 


i'5i 


1-51 


a Ursae Maj . 


I'97 


I- 9 6 


1-95 


1-94 


i -94 


i'93 


I'92 


92 


1-91 


1-91 


1-91 


1-90 


1-90 


1-90 


1-90 


1-90 


S. Decln. 


































Rigel .. 


151 


'ISO 


-150 


149 


149 


148 


I 4 8 


! M7 


147 


147 


147 


146 


146 


146 


146 


146 


Sirius . . 


308 


307 


306 


305 


'33 


303 


302 


301 


300 


300 


299 


299 


298 


298 


298 


298 


e Sagittarii 


710 


7 06 


703 


701 


698 


696 


694 


692 


691 


689 


688 


687 


686 


686 


686 


685 


X Scorpii 


7 8l 


77 8 


774 


77 1 


769 


766 


764 


762 


760 


759 


757 


756 


756 


755 


755 


755 


7 Argus 


I'll 


I'll 


I'lO 


I'lO 


I'lO 


1-09 


I'09 


1-09 


i -08 


i -08 


1-08 


i -08 


i -08 


i -08 


i -08 


i -08 


a Gruis 


I-I3 


I'I2 


I'I2 


I'll 


i'ii 


I'lO 


I'lO 


I'lO 


I'lO 


1-09 


1-09 


1-09 


1-09 


i '09 


1-09 


1-09 


Canopus 


1-36 


I'35 


i'34 


1-34 


i'33 


1-33 


i*33 


1-32 


1-32 


1-32 


1-32 


1-31 


i'3i 


1-31 


1-31 


t'3i 


7 Crucis . . 


i'57 


1-56 


1-56 


1-55 


i'55 


1-54 


i'54 


i'53 


i*53 


i'53 


1-52 


1-52 


1-52 


1-52 


1-52 


t'52 


a Pavonis 


i -60 


i'59 


1-58 


1-58 


*'57 


**57 


1-56 


1-56 


i'55 


i'55 


i'53 


i'55 


i'54 


i'54 


i'54 


i*54 


Achernar 


1*64 


1-63 


1-62 


1-62 


1-61 


1-61 


i -60 


i -60 


i'59 


i'59 


i'59 


i'59 


1-58 


1-58 


1-58 


Rp 


j3 Crucis } 
e. Argus i" 


*74 


173 


1-72 


1-72 


1-71 


1-70 


1-70 


1-69 


1-69 


1-69 


1-68 


1-68 


1-68 


1-68 


1-68 


1-68 


3 Centauri 


1-79 


178 


1-77 


1-77 


!' 7 6 


175 


175 


1-74 


1-74 


J 74 


173 


173 


173 


173 


173 


^73 


a 2 Centauri 


1-83 


1-82 


1-81 


I -80 


i -80 


1-79 


179 


1-78 


1-78 


1-77 


1-77 


1-77 


1-77 


1-77 


1-77 


1-76 


a 1 Crucis . . 


2'OO 


i -99 


1-98 


i -97 


i -97 


196 


i'95 


i'95 


i- 94 


1-94 


1-94 


i'93 


i '93 


i'93 


i'93 


i '93 


aTri. Aus. 


2-68 


2-67 


2-65 


2-64 


2-64 


2-63 


2-62 


2'6l 


2'6l 


2-60 


2-60 


2'59 


2*59 


2'59 


2'59 


2 '59 


Argus .. 


2-75 


273 


272 


2-7! 


2-70 


2-69 2-69 


2-68 


2-67 


2-67 


2-66 


2-66 


2-66 


2-65 


2-65 


2-65 




m. 


m. m. 


m. 


m. 


m. 


ni. 


m. 


m. 


m. 


m. rn. 


m. 


m. m. 


m. 




oo 


56 


5 2 


4 8 


44 


40 


36 


32 


28 


24 


20 I 16 


12 


8 


4 


oo 




7Hr. 


6 HOURS. 



Table A. 

When hour angle is less than 6 hours, name the factors taken from Table A contrary to name of lat. 





HOUR. 


IHr. 


4 












S 


m. 


Var. 

tr T 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




1 


ofL. 


4 


8 


12 


16 


20 


24 


23 


32 


36 


40 


44 


48 


52 


58 


00 







































6i 
62 


413 
431 


17-0 
18-2 


103 

1 08 


52 
54 


It 


26 

27 


21 
21 


17-2 
17-9 


147 


I2'8 


11-4 
11-9 


IO'2 
107 


9'3 

97 


8-5 
8-8 


7-8 
8-1 


7-2 
7'5 


67 
7-0 


63 


450 


19-4 


112 


56 


37 


28 


22 


187 


16*0 


I 4 -0 


12-4 


II'I 




9-2 


8'5 


7-9 


7'3 


64 


470 


20-8 


117 


59 


39 


29 


23 


19*5 


167 


147 


12-9 


n-6 


10-5 




8'9 


8-2 


77 


65 


491 


22-4 


"3 


61 


4I 


31 


25 


20-4 


I7-5 


iV3 


13^ 


I2'2 


II'O 


IO'I 


9'3 


8-6 


8-0 


66 


515 


24-2 


129 


64 


43 


32 


26 


21-4 


18-3 


i6'o 


14-2 


127 


n-6 


io'6 


97 


9-0 


8-4 


67 


540 


26-2 


135 


67 


45 


34 


27 


22'4 


19-2 


16-8 


14-9 


13*4 


I2'I 


ii'i 


IO'2 


9*4 


8-8 


68 


567 


28-6 


142 




47 


35 


28 


23*5 


20*2 


17-6 




I 4 -0 


127 


ii-6 


I0'7 


9'9 


9-2 


69 


597 


31-2 


I 4 9 


75 


50 


37 


30 


2 4 '8 


21'2 


18-5 


16-4 


I 4 '8 


I3'4 


12-3 


11-3 


10*4 


97 


70 


630 


34-3 


157 


79 


52 


39 


31 


26'I 


22*4 


I9-5 




15-6 


I4'I 


I2'9 


ii'9 


II'O 


10-3 


7i 


666 


37-8 


166 


83 


55 


42 


33 


27*6 


237 


207 


18-3 


16-5 


I4'9 


J 37 


I2'6 


ii-6 


10-8 


72 


75 


42-0 


176 


88 


59 


44 


35 


29-3 


25-1 


21-9 


19-4 




15*8 


14-6 


13-3 


12-3 


"'5 




m. 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




59 




56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


oo 




11 HOURS. 





1 HOUR. 


2Hr. 


5 


m. 


m. 


m. 


m. 


m. 


rn. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




00 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 


61 


67 


6'3 


5*9 


.5'5,5 


5'24 


4*96 


470 


4*47 


4'25 


4*05 


3-87 


370 


3*54 


3-39 


3*25 


3-12 


62 


7'0 


6-6 


6-2 


579 


5H6 


5*17 


4-90 


4-65 


4*43 


4-22 


4*03 


3-86 


3-69 


3 '54 


3 '39 


3-26 


63 


7*3 


6-8 


6-4 


6'04 


570 


5*39 


5' 1 1 


4-86 


4-62 


4-41 


4'2I 


4-02 


3-85 


3-69 


3' 54 


3*4 


64 


77 


7-2 


67 


6-31 


5'95 


5-63 


5*34 


5*07 


4-83 


4-61 


4-40 


4-20 


4-02 


3-86 


37 


3*55 


65 


8-0 


7'5 


7-0 


6-60 


6-23 


5-89 


5'59 


5'3i 


5-05 


4-82 


4-60 


4-40 


4-21 


4*03 


3-87 


37i 


66 


8-4 


7-8 


7*3 


6-91 


6-52 


6-17 


.5-8.5 


5-56 


5-29 


5'04 


4-82 


4-61 


4-41 


4-22 


4'05 


3-89 


67 


8-8 


8-2 


77 


7'25 


6-84 


6-47 


6-14 


5-83 


5'55 


5'29 


5'05 


4-83 


4-62 


4'43 


4'25 


4-08 


68 


9-2 


8-6 




7-62 


7-19 


6-80 


6'45 


6-13 


5-83 


5-56 


5-3I 


5-07 


4-86 


4-65 


4*47 


4-29 


69 


97 


9-1 


8'5 


8-02 


7 '57 


7-16 


679 


6'45 


6-14 


5-85 


5'59 


5'34 


5'" 


4-90 


470 


4'5i 


70 


10-3 


9'6 


q-o 


8-46 


7'98 


7">5 


7-16 


6'8o 


6-47 


6-17 


5-89 


5-63 


5' 39 


5-17 


4-96 


476 


7i 


10-8 


IO'I 


9'5 


8-94 


8-43 


7-98 


7*57 


7-19 


6-84 


6-52 


6-23 


5'95 


570 


5H6 


5*24 


5-03 


72 


ii'5 


107 


IO'I 


9'47 


8-94 


8- 4 6 


8'02 


7-62 


7*25 


6-91 


6'6o 


6-31 


6-04 


579 


5*55 


5'33 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


oo 




11 Hr. 


10 HOURS. 





2 HOURS. 


3Hr. 


3 










m. 


m. 


m. 


m. 


m. 


m. 


in. 


m. 


m. 


m 


m. 


ra. 


m. 


m. 


in. 


m. 




00 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 











i 


i 


i 


/ 


i 


i 


i 


i 


/ 


i 


t 


t 


t 


61 


3-12 


3*oo 


2-89 


278 


2-67 


2-58 


2- 4 8 


2-39 


2-31 


2-23 


2-15 


2'08 


2*OO 


i'93 


I-8 7 


1-80 


62 


3'26 


3'i3 


3-01 


2-90 


279 


2-69 


2'59 


2-50 


2-41 


2-32 


2-24 


2*16 


2-09 


2'02 


I'95 


1-88 


63 


3-40 


3-27 


3'I4 


3'02 


2-91 


2'8o 


270 


2'6o 


2-51 


2-42 


2'34 


2-26 


2-18 


2'IO 


2-03 


1-96 


64 


3'55 


3'4i 


3-28 


3-i6 


3*04 


2'93 


2-82 


272 


2-62 


2'53 


2-44 


2-36 


2-28 


2-20 


2'12 


2-05 


65 
66 


37 1 
3-89 


3'57 
374 


3*43 
3*59 


3-30 
3H6 


3'i8 
3*33 


3'06 
3'2i 


2'95 
3*09 


2-8 5 
2-98 


HJ 


2-65 
277 


2-56 
2-68 


2-47 
2-58 


2-38 

2-49 


2-30 
2'4I 


2'22 
2'33 


2-14 
2-25 


67 


4-08 


3-92 


377 


3-63 


3'49 


3-36 


3*24 


3'13 


3-02 


2*91 


2-81 


271 


2-02 


2'53 


2-44 


2-36 


68 


4*29 


4-12 


3-96 


3'8i 


3-67 


3-53 


3H 1 


3-28 


3'i7 


3-o6 


2'95 


2-85 


275 


2-65 


2' 5 b 


2-48 


60 


4'5i 


4'34 


4-17 


4-01 


3'86 


372 


3'59 


3H6 


3*33 


3'22 


3'io 


3-00 


2-89 


279 


270 


2-61 


70 


476 


4*57 


4'40 


4'23 


4-07 


3-92 


378 


3*65 


3'52 


3*39 


3*27 


3-ib 


3*05 


2'95 


2-8 5 


275 


7 1 


5'03 


4-83 


4-65 


4'47 


4'3i 


4^5 


4-00 


3-85 


372 


3'59 


3'4 


3'34 


3'23 


3'ii 


3'01 


2-90 


72 


5'33 


5- 12 


4'93 


474 


4-56 


4-40 


4*24 


4-08 


3*94 


3'8o 


3'07 


3*54 


3-42 


3'30 


3-19 


3-08 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


oo 




10 Hr. 


9 HOURS. 



When hour angle is more than 6 hours, name the factors taken from Table A the same as the 
name of the latitude. 



Table A. 

When hour angle is less than 6 hours, name the factors taken from Table A contrary to name of lat. 



-3 


3 HOURS. 


4Hr. 


<8 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


ni. 




00 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 


o 

61 


I -80 


1-74 


1-68 


1-62 


'57 


'SI 


1-46 


1-41 


36 


i 

31 


26 


/ 

I'22 


i 

17 


t 
1-13 


ro8 


i 

1-04 


62 


1-88 


1-82 


i'75 


I-6 9 


63 


5 


1-52 


'47 


M2 


'37 


32 


1-27 


22 


1-18 


1-13 


1-09 


01 


1-96 


1-90 


1-83 


1-77 


71 


65 


i '59 


53 


48 


- 43 


"37 


32 


27 


1*23 


1-18 


1-13 


64 


2-05 


1-98 


1-91 


I-8 5 


78 


72 


1-66 


60 


55 


'49 


'44 


38 


33 


1-28 


1-23 


ri8 


65 


2-14 


2-07 


2-00 


i'93 


86 


80 


1-74 


68 


62 


56 


'50 


'45 


39 


i'34 


1-29 


1-24 


56 


2-25 


2-17 


2'O9 


2'O2 


'95 


88 


1-82 


'75 


69 


63 


'57 


'SI 


46 


1-40 


i*35 


1-30 


67 


2-36 


2-28 


2'2O 


2'12 


2-05 


98 


1-91 


84 


78 


71 


65 


59 


'53 


1-47 


1-42 


1-36 


68 


2-48 


2'39 


2-31 


2-23 


2-15 


2-08 


2-00 


'93 


87 


80 


73 


67 


61 


i'55 


1-49 


i '43 


69 


2*61 


2-52 


2'43 


2'35 


2-26 


2-19 


2'II 


2-04 


1-96 


1-89 


82 


76 


69 


1-63 


i'57 


1-50 


70 


2'75 


2-6 5 


2- 5 6 


2-47 


2-39 


2-31 


2*22 


2-15 


2-07 


2'00 


92 


85 


78 


1-72 


1-65 


i '59 


7 1 


2-90 


2'8o 


2-7I 


2'6l 


2-52 


2-44 


2'35 


2-27 


2-19 


2'II 


2-03 


96 


'89 


1-81 


i*75 


1-68 


72 


3'08 


2-97 


2-8 7 


2'77 


2-68 


2- 5 8 


2'49 


2-40 


2-32 


2-24 


2-16 


2-08 


2'OO 


1-92 


1-85 


1-78 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 


52 


4 8 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


oo 




9Hr. 


8 HOURS. 





4 HOURS. 


5Hr. 



,_3 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




00 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 





i 










i 






i 


t 


t 












61 


I-0 4 


I'OO 


96 


92 


88 


84 


80 


'77 


'73 


69 


66 


62 


*59 


55 


52 


48 


62 


1-09 


1*04 


I'OO 


96 


92 


88 


84 


80 


76 


72 


68 


6s 


61 


'57 


*54 


"SO 


63 


1-13 


1-09 


04 


oo 


96 


92 


8 7 


83 


'79 


'75 


71 


68 


64 


60 


56 


'53 


64 


1-18 


1-14 


09 


04 


I'OO 


96 


91 


87 


83 


79 


'75 


71 


67 


63 


'59 


55 


65 


24 


1-19 


>;r 4 


09 


1-05 


oo 


*95 


91 


87 


82 


78 


'74 


70 


66 


61 


57 


66 


'30 


i'34 


19 


-I 4 


I'lO 


05 


oo 


'95 


91 


86 


82 


'77 


"73 


69 


64 


60 


67 


36 


1-31 


25 


20 


i'i5 


10 


05 


oo 


'95 


90 


86 


81 


'77 


72 


68 


63 


68 


'43 


i'37 


32 


26 


1*21 


15 


10 


05 


I'OO 


'95 


90 


'85 


80 


76 


71 


66 


69 


50 


1-44 


'39 


'33 


1-27 


21 


16 


ii 


1-05 


I'OO 


95 


90 


85 


80 


*75 


70 


7 


59 


1-52 


46 


4 o 


1*34 


28 


22 


17 


I'll 


1-05 


I'OO 


'95 


89 


'84 


'79 


*74 


7i 


68 


1-61 


54 


48 


1-42 


35 


I'29 


23 


1-17 


i'ii 


i'o6 


I'OO 


'94 


89 


83 


78 


72 


78 


1-71 


64 


'57 


1-50 


'44 


i*37 


31 


1-24 


1-18 


I" 12 


i -06 


I'OO 


'94 


88 


82 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


00 




8Hr. 


7 HOURS. 





5 HOURS. 


6Hr. 


i 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m 


rn. 


m. 


m. 


m. 


m. 


m. 




00 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 


o 
























l 


( 


( 


f 


i 


61 


483 


450 


416 


383 


351 


318 


286 


254 


222 


190 


158 


126 


095 


06 3 


031 


ooo 


62 


504 


469 


'434 


400 


366 


332 


298 


264 


2 3 I 


198 


165 


I 3 2 


099 


066 


033 


ooo 


63 


526 


489 


'453 


417 




346 


311 


2 7 6 


2 4 I 


206 


172 


137 


103 


069 


034 


ooo 


64 


'549 




'473 


436 


399 


362 


325 


288 


252 


215 


179 


143 


107 


072 


036 


ooo 


65 
66 


'575 
602 


535 

560 


'495 
519 


456 

'477 


417 

*437 


378 
396 


340 

356 


301 
316 


263 


225 
2 3 6 


188 
197 


150 
157 


112 

118 


075 

078 


037 
039 


ooo 
ooo 


67 


631 


587 


'544 


501 


458 




373 


331 


289 


248 


206 


165 


123 


082 


4 I 


ooo 


68 


663 


617 


571 


526 


48! 


436 


'392 


348 


304 


260 


217 


173 


130 


086 


043 


ooo 


69 


698 


650 


601 


'554 


506 


'459 


413 


366 


320 


274 


228 


!82 


137 


091 


045 


ooo 


7 


736 


685 


634 


584 


534 


484 


'435 


386 


'337 


289 


240 


192 


144 


096 


048 


ooo 


7 1 


778 


724 


670 


617 


565 


512 


460 


408 


'357 


305 


254 


203 


152 


101 


051 


ooo 


72 


825 


767 


711 


'654 


5Q8 




487 


'433 


378 


323 


269 


215 


161 


107 


054 


ooo 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


oo 






6 HOURS. 



When hour angle is more than 6 hours, name the factors taken from Table A the same as the 
name of the latitude. 



Table A. 
vVheu hour angle is less than 6 hours, name the factors taken from Table A contrary to name of lat. 







HOUR. 


IHr. 


5 

i* 


in. 


Var. 


m. 


m. 


m. 


m. 


m. 


in. 


m. 


in. 


m. 


m. 


m. 


rn. 


m. 


m. 


m. 




1 


ofL. 


4 


8 


12 


16 


20 


24 


23 


32 


36 


40 


44 


43 


52 


56 


00 







































73 


750 


47 


I8 7 


94 


62 


47 


37 


31 


26'6 


23'3 


207 


.8.., 


16-8 


!5'4 


14-2 


13*1 


I2'2 


74 


799 


53 


200 


100 


67 


5 


40 


33 


28-4 


24-8 


22'0 


19-8 


17-9 


16-4 


15*1 


14-0 


I3-0 


75 


8.55 


60 


2I 4 


107 


7 1 


53 


43 


36 


30'4 


26-6 


23-6 


21'2 


19*2 


I 7 '6 


16-2 


15-0 


13*9 


76 


919 


69 


2 3 


H5 


77 


57 


46 


38 


327 


28-5 


25-3 


22'7 


2O'6 


18-9 


17-4 


16-1 


15-0 


77 


993 


80 


2 4 8 


124 


83 


62 


50 


4i 


35'3 


30-8 


27-3 


24-6 


22'3 


20-4 


18-8 


17-4 


16-2 


78 


1078 


93 


270 


135 


90 


67 


54 


45 


38'3 


33'5 


29*7 


267 


24-2 


22'I 


20-4 


18-9 


I 7 -6 


79 


1179 


111 


295 


H7 


98 


74 


59 


49 


41-9 


36-6 


32'5 


2Q-2 


26-5 


24 '2 


22-3 


20-6 


I9-2 


80 


1300 


134 


325 


162 


108 


81 


65 


54 


46-2 


40-4 


35-8 


32-2 


29-2 


26-7 


24-6 


22-7 


21*2 


81 


J 447 


165 


362 


181 


120 


90 


72 


60 


5IH 


44'9 


39'9 


35-8 


32*5 


29*7 


27-3 


25-3 


23-6 


82 


1631 


210 


408 


204 


1.36 


102 


81 


68 


58-0 


50-6 


44'9 


4'4 


36-6 


33*5 


30-8 


28-5 


26-6 


*3 


1867 


275 


467 


233 


155 


116 


93 


77 


66-3 


58-0 


5i-4 


46-2 


4 I-9 


38-3 


35-3 


32-7 


30H 


84 


2181 


377 


.545 


272 


181 


136 


109 


9i 


77'5 


67-7 


60- 1 


54'o 


48-9 


44-8 


41-2 


38-2 


35'5 


8s 


2620 


548 


655 


327 


218 


163 


131 


109 


93'i 


8i'3 


72-2 


6 4 -8 


58-8 


53-8 


49-5 


45-8 


427 




m. 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




59 




56 


52 


4 8 


44 


40 


36 


32 


28 


24 


20 


L6 


12 


8 


4 


oo 




11 HOURS. 





1 HOUR. 


2Hr. 


,1 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




00 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 52 


56 


00 


o 


































73 


I2'2 


II'4 


io'7 


lO'I 


9*5 


9-0 


8'5 


8-1 


77 


7'3 


7-0 


6-7 


6-4 


6-2 


5'9 


5'7 


74 


13-0 


I2'2 


11-4 


10-7 


lO'I 


9-6 


9-1 


8-6 


8'2 


7-8 


7*5 


7-2 


6-8 


6-6 


6-3 


6-0 


75 


I3-9 


13-0 


I2'2 


ii-5 


10-8 


10-3 


97 


9-2 


8-8 


8-4 


8-0 


7'7 


7*3 


7-0 


6-7 


6'5 


76 


I5'0 


I 4 '0 


I3-I 


12-3 


n-6 


I I'D 


10-4 


9*9 


9H 


9-0 


8-6 


8-2 


7*9 


7*5 


7-2 


6' 9 


77 


16-2 


I5'I 


I 4 -2 


I3'3 


I2'6 


II-Q 


1 1 -3 


107 


IO'2 


9'7 


9\3 


8'9 


8'5 


8-1 


7-8 


7'5 


78 


17-6 


16-4 


J 5'4 


*4'5 


13*7 


I2'9 


12-3 


n-6 


II'I 


10*6 


IO*I 


9'6 


9-2 


8-8 


8'5 


8-2 


79 


10/2 


I7-9 


16-8 


15-8 


14-9 


I 4 'I 


i3'4 


12-7 


I2'I 


n-6 


II'O 


10-5 


lO'I 


9-7 


9'3 


9-0 


80 


21*2 


I9'8 


18-5 


i7'5 


16-5 


i5'6 


14-8 


14-0 


13*4 


12-7 


I2'2 


u-6 


ii-i 


10-7 


10*2 


9-8 


8 1 


23-6 


22 'O 


20-7 


19-4 


18-3 


I7-3 


16-4 


15-6 


I4'9 


14-2 


I3-5 


12-9 


12-4 


II-Q 


II'4 


10-9 


82 


26-6 


.24-8 


23-3 


21-9 


20-7 


I9'5 


1*3 


17-6 


16-8 


i6'o 


1.5-3 


14-6 


14-0 


I3H 


I2'8 


12-3 


8^ 


30-4 


28- 4 


26-6 


25-1 


237 


22-4 


21-7 


2O'2 


19-2 


18-3 


i7'5 


16-7 


i6'o 


I5-3 


14-7 


14-1 


84 


35*5 


33'2 


31-1 


29-3 


27-6 


26-1 


24-8 


23*5 


22-4 


21-4 


20-4 


I9'5 


18-7 


17-9 


17-2 


16-5 


85 


42-7 


39'9 


37'4 


35'2 


33'2 


3i'4 


29-8 


28-3 


26-9 


25*7 


24-5 


23'4 


22-4 


21-5 


20'6 


19-8 




m. 


m. j m. 


m. 


m. 


m. 


m. 1 m. 


m. 1 m. 


m. 


m. 


m. m. | m. 


m. 




00 


56 


52 


48 


44 


40 


36 1 32 


28 | 24 


20 


16 


12 | 8 


4 


00 




11 Hr. 


10 HOURS. 






2 HOURS. 


3Hr. 


,1 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m 


m. 


m. 


m. 


m. 


m. 


m. 




00 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 


o 






i 


i 


i 


i 


i 


i 


i 


i 


i 


i 


i 


i 


i 


i 


73 


5'7 


5'4 


5'2 


5*o 


4'8 


4'7 


4'5 


4'3 


4*2 


4-0 


3*9 


3*8 


3'6 


3'5 


3'4 


3*3 


74 


6-0 


5'8 


5'6 


5'4 


5'2 


5'0 


4'8 


4-6 


4*5 


4*3 


4-2 


4-0 


3*9 


3'7 


3-6 


3*5 


75 


6\5 


6-2 


6-0 


5*7 


5'5 


5'3 


5'i 


5'0 


4'8 


4-6 


4*4 


4'3 


4'i 


4-0 


3'9 


3'7 


76 


6-9 


6-7 


6-4 


6'2 


5*9 


5'7 


5'5 


5'3 


5'i 


5*0 


4'8 


4-o 


4'5 


4'3 


4-2 


4-0 


77 


7*5 


7-2 


6-9 


6-7 


6-4 


6'2 


6-0 


5'7 


5'5 


5'3 


5'2 


5-0 


4-8 


4-6 


4-5 


4*3 


78 


8-1 


7'8 


7'5 


7-2 


7-0 


6-7 


6-5 


6-2 


6-0 


5-8 


5'6 


5'4 


5'2 


5'0 


4-9 


4'7 


79 


8-9 


8-6 


8-2 


7-9 


7-6 


7*3 


7-1 


6-8 


6-6 


6-4 


6-1 


5'9 


5*7 


5\5 


5'3 


5'i 


80 


9-8 


9'4 


9*1 


8-7 


8'4 


8-1 


7*8 


7*5 


7'3 


7-0 


6-8 


6'5 


6-3 


6-1 


5'9 


5'7 


81 


io'9 


10-5 


lO'I 


9*7 


9*4 


9-0 


8-7 


8-4 


8-1 


7'8 


7'5 


7'3 


7-0 


6-8 


6'5 


6-3 


82 


12-3 


ii-8 


11-4 


II'O 


10-5 


IO'2 


9*8 


9*4 


9-1 


8-8 


8'5 


8-2 


7-9 


7-6 


7'4 


7-1 


83 


14-1 


13-6 


13-0 


12-5 


I2'I 


11-6 


II-2 


10-8 


10-4 


IO*I 


9*7 


9'4 


9-0 


8-7 


8-4 


8-1 


8 4 


16-5 


15-8 


15-2 


14-7 


I4'I 


13-6 


I3'I 


I2'6 


12-2 


11-7 


11-3 


10-9 


io'6 


IO'2 


9-9 


9'5 


85 


19-8 


19-0 


18-3 


17-6 


l6'9 


16-3 


157 


15-2 


I 4 '6 


14-1 


13-6 


13-1 


12-7 


12-3 


1 1 -8 


n-4 




m. 


m. 1 m. 


m. j m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 1 52 


48 1 44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


oo 




10 Hr. 


9 HOURS. 



When hour angle is more than 6 hours, name the factors taken from Table A the 5am* as the 
of the latitude. 



Table A. 

When hour angle is less than 6 hours, name the factors taken from Table A contrary to name of lat. 



. 


3 HOURS. 


4Hr. 


s 

(-4 


m. 


rn. [ m. 


m. 


m. 


m. 


m. 


m. in. 


m. 


m. 


m. 


m. 


m. 


in. 


m. 




00 


4 8 


12 


16 


20 


24 


23 ! 32 


36 


40 


44 


43 


52 


56 


00 





































73 


3-3 


3'2 


3'I 


2'9 


2-8 4 


2'74 


2-6 5 


2' 5 6 


2-46 


2- 3 8 


2-29 


2'2I 


2'12 


2-04 


1-97 


1-89 


74 


3-5 


3'4 


3'3 


3'i 


3'03 


2'93 


2-82 


2-72 


2-63 


2'53 


2*44 


2'35 


2-26 


2-18 


2'10 


2'01 


75 


3-7 


3-6 


3*5 


3'4 


3'24 


3'i3 


3 -02 


2-92 


2-81 


2-71 


2-61 


2-52 


2- 4 2 


2'33 


2'24 


2-15 


76 


4-0 


3'9 


3'7 


3-6 


3*49 


3'37 


3-25 


3-I3 


3-02 


2-91 


2-81 


271 


2'60 


2-51 


2-4I 


2'32 


77 


4*3 


4-2 


4*o 


3*9 


3'77 


3'63 


3-5I 


3-38 


3-26 


3'i5 


VQ3 


2-92 


2-81 


2-71 


2'6o 


2-50 


78 


4'7 


4*5 


4*4 


4*2 


4-09 


3'95 


3-81 


3'68 


3'55 


3M2 


3-29 


3-17 


3-06 


2-94 


2-8} 


272 


79 


5'i 


5'0 


4'8 


4-6 


4'47 


4-32 


4-17 


4 -02 


3'88 


374 


3-60 


3'47 


3*34 


3-21 


3-09 


2'97 


80 


57 


5'5 


5'3 


5'i 


4*93 


4-76 


4*59 


4'43 


4-27 


4-12 


3-97 


3-83 


3-68 


3*54 


3-41 


3'27 


81 


6'3 


6-1 


5 '9 


5*7 


5*49 


5'30 


5'n 


4'93 


4-76 


4*59 


4*42 


4-26 


4-10 


3*95 


3'79 


3^5 


82 


7-1 


6-9 


6-6 


6-4 


6-19 


5'97 


5-76 


5'56 


5-36 


5-17 


4-98 


4-80 


4*62 


4*45 


4-28 


4-1 1 


8} 


8-1 


7*9 


7-6 


7'3 


7-08 


6-83 


6-60 


6-36 


6-14 


5'Q2 


5-70 


5*49 


5-29 


5'09 


4'8q 


47 


84 


9'5 


9-2 


8-9 


8-6 


8-27 


7-98 


7-70 


7'43 


7-17 


6-91 


6-66 


6-42 


6-18 


5'95 


572 


5*49 


83 


n- 4 


II'O 


107 


10-3 


9'94 


9'59 


9-26 


8-93 


8-61 


8-30 


8-00 


771 


7M2 


7-14 


6-87 


6-60 




m. 


m. 


m. 1 m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 


52 1 48 


44 


40 


36 


32 


28 


2 4 


20 


16 


12 


8 


4 


00 




9 Ki- 


8 HOURS. 





4 HOURS. 


5Hr 


5 


m. 


m. 


m. 


DQ. 


m 


m 


m. 


m 


m 


m. 


m 


m. 


m. 


m. 


m. 


m. 




00 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 




73 


,8 9 


i-8i 


174 


1-67 
















i 
13 


06 


4 

I'OO 


4 

'94 


88 


I -60 


1-53 


I- 4 6 


1*39 


32 


1-26 


I-I9 


74 


2'OI 


i '93 


1-85 


178 


170 


I'6 3 


1*55 


1-48 




i'34 


1-27 


20 


13 


07 


oo 


'93 


75 


2-15 


2-07 


1-98 


1-90 


1-82 


174 


i-66 




'Si 






29 


*2I 


14 


07 


1*00 


7 6 


2-32 


2'22 


2:13 


2 '04 


1-96 


l-8 7 


179 


170 


62 


I *54 


I- 4 6 


38 


30 


23 


15 


1-07 


77 


2-50 


2- 4 


2-30 


2'2I 


2*11 


2 'O2 


1-93 


1-84 


75 


1-66 


1-58 


"49 


'4 1 


32 


24 


16 


78 


272 


2'6l 


2-50 


2-40 


2-29 


2'19 


2-09 


2'OO 


90 


1-81 


171 


62 


'53 


44 


'35 


26 


79 


2'97 


2*85 


274 


2-62 


2-51 


2*40 


2-29 


2-18 


2-08 


1-97 


1-87 


77 


67 


57 


48 


38 


8o 


3-27 


3'M 


3-02 


2-89 


2'77 


2-6 4 


2'53 


2- 4 I 


2 29 


2-18 


2'06 


'95 


84 


73 


1-63 


52 


81 


3-65 


3-50 


.V36 


3'22 


3-08 


2-94 


2'8l 


2-68 


2*55 


2-42 


2-30 


2-17 


2-05 


1-93 


1-81 


69 


82 


4-11 


3'94 


3-78 




3'47 


3-32 


3-I7 


3-02 


2-87 


273 


2'59 


2'45 


2-31 


2-18 


2-04 


91 


83 


470 


4-5I 


4'33 


4-15 


3 '97 


3'8o 


3-63 


3-46 


3-29 


3-13 


2-96 


2-80 


2-65 


2*49 




2-18 


84 


5 '49 


5-27 


5-06 


4'85 


4-64 


4'44 


4-24 


4-04 


3-84 


3-65 


3-46 


3-28 


3-09 


2-91 


273 


2-55 




6-60 


6-34 


6-08 


5-82 


5'57 


5-33 


5-09 


4-85 


4-62 


4'39 


4-16 


3'94 


3-7I 


3*49 


3-28 


3-06 




m 


m 


m 


m 


m. 


m 


m 


m. 


m. 


m. 


m. 


m 


m. 


m. 


m. 


m. 




oo 


56 


52 


48 


44 


4 o 


36 


32 


28 


24 


20 


16 


12 


8 


4 


oo 




8Hr 


7 HOURS. 





5 HOURS 


GHr. 


5 


m. 


m 


m. 


m 


ua 


to 


m 


m 


m. 


m 


m. 


m. 


m. 


m. 


m. 


m. 




00 


4 


8 


12 


18 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 





. 


. 


4 


4 


4 


i 


4 


4 


4 


4 


4 


4 


4 


4 


4 


4 


73 


88 


82 


76 


70 


6 4 


58 


52 


4 6 


40 


'34 


29 


'23 


17 


'II 


06 


oo 


74 


93 


87 


81 


74 


68 


61 


'55 


*49 


*43 


'37 




24 


18 


12 


06 


oo 


75 


I'OO 


93 


86 


79 


73 


66 


'59 


52 


46 


39 


'33 


26 


20 


13 


07 


oo 


76 


1-07 


I'oo | 93 


85 


78 


71 


64 


56 


'49 


42 


'35 


28 


21 


' J 4 


07 


oo 


77 


16 


i -08 


I'OO 


92 


84 


76 


69 


61 


"53 


46 


38 


3 


23 


15 


08 


oo 


78 


26 


17 


09 


I -00 


91 


83 


'75 


66 


58 


'49 


41 




25 


16 


'OS 


oo 


79 


38 


28 


19 


1-09 


oo 


91 


8 1 


72 


63 


'54 


'45 


36 


2 7 


18 


09 


oo 


80 


52 


'4 1 


'3 1 


I-2I 


10 


I'OO 


90 


80 


70 


60 


"SO 


40 


3 


20 


10 


oo 


81 


69 


*57 


46 


J *34 


23 


i'n 


oo 


89 


78 


66 


*55 


44 


'33 


22 


II 


oo 


82 


91 


'77 


64 


1-51 


38 


1*25 


13 


I'OO 


87 


75 


62 


50 


*37 


25 


'12 


oo 


83 


2-18 


2-03 


QQ 
OO 


i'73 


58 


1-44 


29 


1*14 


I'OO 


86 


71 


57 


'43 


'28 


14 


oo 




2'55 


2'37 


2'2O 


2'O2 


85 


1-68 




i'34 


1-17 


I'OO 


83 


67 


50 


'33 


17 


oo 


85 


3'o6 


2-85 


2-64 


2'43 


2'22 


2'O2 


81 




1*40 


I'20 


i -go 


80 


60 


40 


20 


oo 




in. 


m. 


m. 


m. 


m. 


m. 


m. 


m. I m. 


m. 


rn. 


m. 


m. 


m. 


m. 


m. 




oo 


56 


25 


48 


44 


40 


36 


32 1 28 


24 


20 


16 


12 


8 


4 


oo 




7Hr. 


6 HOURS. 



When hour angle is more than 6 hours, name the factors taken from Table A the same as the 
lame of the latitude. 



Table B. 

Always name the factors taken from Table B the same as the name of declination. 



1 


HOUR. 


1 Hr. 


15 

c 




Var. 


































m. 


to 1' 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


I 


1 


of 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


58 


00 


Q 




Decl. 




































































30 


132 


5-33 


33'i 


16-5 


iro 


8-28 


6-62 


5-52 


474 


4^5 


3-69 


3*32 


3-03 


278 


2'57 


2-39 


2-23 


31 


138 


5-44 


34H 


17-2 


n'5 


8-61 


6-89 


575 


4'93 


4-32 


3-84 


3H6 


3'I5 


2-89 


2-67 


2- 4 8 


2-32 


32 


143 


5'56 


35-8 


17-9 


11-9 


8-96 


7-17 


5-98 


5^3 


4'49 


3'99 


3'6o 


3-27 


3-01 


278 


2-58 


2-41 


33 


149 


5-69 


37'2 


18-6 


12-4 


9-3i 


7'45 


6-21 


5'33 


4-67 


4^5 


374 


3-40 


3'i2 


2-89 


2-68 


2-51 


34 


155 


5'82 


38-6 


I9'3 


12-9 


9-67 


774 


6-45 


5'53 


4^5 


4'3 J 


3'88 


3'53 


3'24 


3-00 


279 


2'6l 


35 


160 


5-96 


40-1 


2O'I 


13*4 


IO'O 


8-03 


670 


575 


5-03 


4-48 


4'3 


3-67 


3'37 


3-11 


2-89 


271 


36 


167 


6-11 


41-6 


20-8 


13-9 


10-4 


8-34 


6'95 


5'96 


5-22 


4-64 


4-18 


3-81 


3'49 


3-23 


3-00 


2'8l 


37 


173 


6-27 


^3'2 


21-6 


14-4 


10-8 


8-65 


7-21 


6-18 


5HI 


4-82 


4*34 


3'95 


3-62 


3'35 


3-11 


2-91 


38 


179 


6-44 


44-8 


22- 4 


14-9 


II'2 


8-96 


7'47 


6-41 


5'6i 


4*99 


4'50 


4-09 


376 


3'47 


3-23 


3-02 


39 


1 86 


6-62 


46-4 


23-2 


i5'5 


n-6 


9-29 


775 


6-64 


5-82 


5-i8 


4-66 


4-24 


3-89 


3-60 


3*35 


3*13 


40 


192 


6-82 


48-1 


24-0 


16-0 


I2'O 


9-63 


8-03 


6-89 


6*03 


5-36 


4-83 


4-40 


4-04 


373 


3'47 


3-24 


4i 


199 


7-03 


49-8 


24-9 


16-6 


I2'5 


9'97 


8-32 


7 >:t 3 


6-25 


5-56 


5'oi 


4-56 


4-18 


3-86 


3'59 


3-36 


42 


206 


7'25 


5i-6 


2 5 -8 


17-2 


12-9 


10-3 


8-61 


7'39 


6-47 


576 


5'i9 


472 


4'33 


4-00 


37 2 


3-48 


43 


214 


7-48 


53'4 


267 


17-8 


13-4 


107 


8-92 


7-65 


670 


5-96 


5'37 


4-89 


4'49 


4'JS 


3-85 


3-60 


44 


221 


7'73 


55'3 


277 


18-5 


13-8 


ii'i 


9 ! 24 


7-92 


6-94 


6-17 


5-56 


5-o6 


4-64 


4-29 


3'99 


373 


45 


229 


8-00 


57'3 


287 


19-1 


I4'3 


H'5 


9'57 


8-21 


7-19 


6-39 


576 


5-24 


4-81 


4'45 


4 -I 3 


3'86 


46 


237 


8-29 


59'3 


297 


19-8 


14-8 


11-9 


9-91 


8-50 


7'44 


6-62 


5-96 


5'43 


4-98 


4-60 


4-28 


4-00 


47 


246 


8-60 


61-4 


30-7 


20-5 


^4 


12-3 


10-3 


8-80 


771 


6-86 


6-18 


5-62 


5'i6 


477 


4'43 


4-14 


48 


255 


8-93 


63-6 


SI'S 


21'2 


I5-9 


127 


10-6 


9-11 


7-98 


7-10 


6'4O 


5-82 


5'34 


4'94 


4'59 


4-29 


49 


26 4 


9'30 


65-9 


33' 


22'0 


16-5 


13-2 


II'O 


9'44 


8-27 


7*35 


6-62 


6-03 


5'53 


5'ii 


476 


4'44 


50 


273 


9'69 


68-3 


34' J 


22-8 


17-1 


137 


11-4 


978 


8-56 


7-62 


6-86 


6-25 


573 


5-30 


4'93 


4-60 


51 


283 


10-1 


70-8 


35'4 


23-6 


177 


14-2 


n-8 


IO'I 


8-87 


7-89 


7-11 


6-47 


5'94 


5'49 


5'io 


477 


52 


293 


10-6 


73'3 


36-7 


24'5 


i8'3 


*47 


I2'2 


10-5 


9'2O 


8-18 


7'37 


671 


6-16 


5-69 


5-29 


4'95 


53 


304 


in 


76*0 


38-0 


25-4 


19-0 


15*2 


127 


io'9 


9-54 


8-48 


7-64 


6'95 


6-38 


5-90 


5'49 


5-I3 


54 


315 


11-6 


78-9 


39'4 


26-3 


197 


15-8 


I3-2 


ii'3 


9-89 


8-80 


7'93 


7-21 


6-62 


6-12 


5-69 


5-32 


55 


327 


12-2 


81-8 


40-9 


27-3 


20-5 


16-4 


137 


117 


10-3 


9'i3 


8-22 


7-48 


6-87 


6-35 


5-90 


5-52 


56 


340 


J2-8 


84-9 


42-5 


28-3 


21-3 


17-0 


I 4 -2 


I2'2 


107 


9-48 


8-54 


777 


7^3 


6-59 


6-13 


573 


57 


353 


13'5 


88-2 


44-1 


29H 


22 'I 


177 


147 


I2'6 


II'I 


9-84 


8-87 


8-07 


7-41 


6-85 


6'37 


5'95 


58 


367 


14-3 


91-7 


45'9 


30-6 


22'9 


18-4 


I5-3 


I3-I 


11-5 


IO'2 


9-22 


8'39 


770 


7-11 


6-62 


6-18 


59 


38i 


15'1 


95'4 


477 


31-8 


23-9 


19-1 


15*9 


137 


I2'0 


10-6 


9-58 


872 


8-00 


7-40 


6-88 


6-43 


60 


397 


16-0 


99-2 


49-6 


33'i 


2 4 '8 


19-9 


16-6 


I4-2 


I2'4 


ii'i 


9-97 


9-08 


8-33 


770 


7-16 


6-69 


61 


4*3 


17-0 


103 


5i7 


34'5 


25-9 


207 


17*3 


I 4 '8 


I 3 -0 


ii*5 


10-4 


9'45 


8-68 


8-02 


7-46 


6-97 


62 


43 1 


18-2 


108 


53'9 


35'9 


27-0 


21-6 


18-0 


!5'4 


I3-5 


I2'O 


10-8 


9-86 


9-05 


8-36 


777 


7-27 


63 


450 


19-4 


112 


56-2 


37'5 


28-1 


22-5 


18-8 


16-1 


I 4 'I 


12-5 


11-3 


10-3 


9'44 


872 


8-n 


7-58 


64 


470 


20-1 


II 7 


587 


39'2 


29'4 


23-5 


19-6 


16-8 


147 


I3'I 


ii-8 


107 


9-86 


9-11 


8-48 


7-92 


65 


491 


22'4 


123 


61-4 


41-0 


307 


24-6 


20-5 


17-6 


I 5'4 


137 


12-3 


ii'2 


10-3 


9-53 


8-86 


8-29 


66 


515 


24-2 


129 


64-4 


42-9 


32-2 


25'8 


21-5 


18-4 


16-1 


14-4 


12-9 


n-8 


10-8 


9-98 


9-28 


8-68 


67 


540 


26-2 


135 


67-5 


45'0 


33-8 


27-0 


22-5 


i9'3 


16-9 


i5'i 


13-6 


12-3 


11-3 


10-5 


974 


9-10 


68 


567 


28'6 


I 4 2 


70-9 


47'3 


35'5 


28-4 


237 


20-3 


17-8 


15-8 


i4'3 


13-0 


11-9 


II'O 


IO'2 


9-56 


69 


597 


31-2 


I 4 9 


74-6 


49-8 


37'3 


29-9 


24-9 


21-4 


187 


167 


15-0 


137 


12-5 


n-6 


10-8 


IO'I 


70 


630 


34-3 


157 


787 


52-5 


39-4 


3I-5 


26-3 


22-5 


197 


17-6 


i 5 '8 


14-4 


13-2 


I2'2 


11-4 


io'6 


7 1 


666 


37-8 


166 


83-2 


55'5 


41-6 


33' 3 


27-8 


23-8 


20-9 


18-6 


167 


15-2 


14-0 


I2'9 


I2*O 


II'2 


72 


705 


42-0 


176 


88-2 


58-8 


44-1 


35'3 


29-4 


25-3 


22'I 


197 


177 


16-1 


14-8 


137 


127 


irg 


73 


750 


47 


187 


937 


62-5 


46-9 


37'5 


3i-3 


26-8 


23-5 


20-9 


18-8 


17-1 


157 


i4'5 


I3-5 


12-6 


74 


799 


53 


200 


99-9 


66-6 


5cro 


40-0 


33*4 


28-6 


25-1 


22'3 


2O'I 


18-3 


i6'8 


15*5 


14-4 


13-5 


75 


855 


60 


2I 4 


107 


7i-3 


53*5 


42-8 


357 


30-6 


26-8 


23^ 


21'5 


19-6 


18-0 


16-6 


I5'4 


14-4 


76 


919 


69 


230 


"5 


76-6 


57'5 


46-0 


38-4 


32-9 


28-8 


2 5 -6 


23-1 


2I'O 


I9-3 


17-8 


16-6 


15-5 


77 


993 


80 


248 


124 


82-8 


62-1 


497 


41-4 


35'5 


3I-I 


277 


24-9 


227 20-8 


i9'3 


17-9 


167 


78 


1078 


93 


270 


135 


89-9 


67-4 


54'0 


45'0 


38-6 


33-8 


3 0-I 


27'I 


247 J22'6 


20-9 


19-4 


18-2 


79 


1179 


111 


295 


147 


98-3 


73-8 


59 '0 


49-2 


42-2 


37'0 


32-9 


29'6 


27-0 


247 


22-9 


21-3 


19-9 


80 


1300 


134 


325 


163 


108 


81-3 


65' i 


54'3 


46-5 


407 


36-3 


327 


297 


27'3 


25-2 


23 4 


21-9 


81 


*447 


165 


362 


181 


121 


90-5 


72-4 


60-4 


51*8 


45'4 


40-4 


36-4 


33'I 


30-4 


28-0 


26-1 


24-4 


82 


1631 


210 


408 


204 


136 


.102 


8 1 -6 


68-1 


58-4 


5fl 


45'5 


4 ro 


37'3 


34*2 


31-6 


29-4 


27-5 


83 


1867 


275 


467 


233 


156 


II 7 


93'4 


77-9 


66-8 


58-5 


52-1 


46-9 


427 


39'2 


36-2 


337 


3^5 


84 


2180 


377 


545 


273 


182 


136 


109 


91-0 


78-1 


68-4 


60'8 


54-8 


49'9 


45'8 


4 2 '3 


39'3 


36-8 


85 


2620 


548 


655 


328 


218 


I6 4 


131 


109 


93'8 


82-1 


73' 1 


65-8 


59'9 


55'o 


50-8 


47-2 


44-2 




m. 

59 





m. 
56 


m. 
52 


m. 
48 


m. 
44 


m. 
40 


m. 
36 


m. 
3 2 


m. 

28 


m. 
24 


m. 

20 


m. 
16 


m. m. 

12 8 


m. 

4 


m. 
oo 




11 HOURS. 



29 
Table B. 

Always name the factors taken from Table B the same as the name of declination. 



1 


1 HOUR. 


2 Hrs. 


1 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


"8 

p 


00 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


58 


00 





/ 


i 


t 


/ 


i 




t 


i 






| 


| 


/ 


y 


| 


| 


30 


2*23 


2'O9 


1-97 


1-87 


1-77 


I-6 9 


1-61 


54 


I- 4 8 


! 4 2 


i'37 


I- 3 2 


1-27 


1-23 


1-19 


i*5 


31 


2-32 


2-18 


2'06 


1-94 


l-8 5 


I- 7 6 


1-68 


60 


I- 54 


48 


1-42 


I- 37 


1-32 


1-28 


1-24 


I'2O 


32 


2' 4 I 


2-27 


2-I 4 


2'02 


1-92 


i-8 3 


174 


6 7 


i -60 


'54 


1-48 


1- 43 


I-38 


i'33 


1-29 


25 


33 


2-51 


2- 3 6 


2'22 


2'IO 


1-99 


1-90 


1-81 


73 


1-66 


60 


i'54 


1-48 


I- 43 


1-38 


i'34 


3 


34 


2'6l 


2*45 


2-3I 


2-18 


2-07 


1-97 


1-88 


80 


173 


66 


i -60 


i '54 


i- 4 9 


1-44 


i'39 


'35 


35 


2-71 


2'54 


2-39 


2-27 


2-15 


2-05 


i'95 


87 


179 


72 


1-66 


i -60 


J '54 


1-49 


1-44 


40 


36 


2-81 


2-64 


2' 4 8 


2'35 


2-23 


2'12 


2*03 


'94 


1-86 


79 


172 


1-66 


i -60 


I> 55 


1-50 


'45 


37 


2-91 


273 


2-58 


2'44 


2-31 


2'20 


2*10 


2'OI 


i'93 


85 


178 


172 


1-66 


1-61 


'55 


'5i 


38 


3-02 


2-83 


2-67 


2'53 


2-40 


2-28 


2-18 


2-09 


2'OO 


92 


1-85 


178 


172 


1-66 


61 


56 


39 


3-13 


2'94 


277 


2'62 


2-49 


2'37 


2-26 


2-16 


2-07 


99 


1-92 


1-85 


178 


172 


67 


62 


4 


3-24 


3-04 


2-8 7 


2*72 


2-58 


2'45 


2-34 


2-24 


2-15 


2-06 


1-99 


1-91 


1-85 


179 


73 


68 


4i 


3-36 


3'i5 


2'97 


2'8l 


2-67 


2'54 


2-43 


2'32 


2'22 


2-14 


2-06 


1-98 


1-91 


1-85 


79 


74 


42 


3-48 


3-27 


3'08 


2'gi 


277 


2-6 3 


2-51 


2-40 


2-30 


2'2I 


2-13 


2-05 


1-98 


1-92 


86 


80 


43 


3-60 


3-38 


3-19 


3-02 


2-86 


273 


2-60 


2'49 


2'39 


2'29 


2'2I 


2-13 


2-05 


1-99 


92 


87 


44 


373 


3'5o 


3'3<> 


3 II 3 


2'97 


2-82 


2-69 


2- 5 8 


2'47 


2'37 


2-29 


2-20 


2-13 


2-06 


'99 


'93 


45 


3-86 


3-63 


3*42 


3-24 


3 ! 7 


2-92 


279 


2-6 7 


2- 5 6 


2- 4 6 


2'37 


2-28 


2-20 


2-13 


2-06 


2-00 


46 


4-00 


3-76 


3'54 


3'35 


3'i8 


3-03 


2-89 


276 


2-65 


2'55 


2'45 


2- 3 6 


2-28 


2'2I 


2-14 


2-07 


47 


4-14 


3-89 


3-67 


3'47 


3-29 


3' r 4 


2-99 


2-86 


274 


2-64 


2'54 


2'45 


2- 3 6 


2-28 


2'2I 


2-I 4 


48 


4-29 


4-03 


3-80 


3'59 


S'4 1 


3-25 


3-10 


2-96 


2-84 


273 


2-6 3 


2'53 


2'45 


2'37 


2'29 


2'22 


49 


4'44 


4-17 


3'93 


372 


3'53 


3-36 


3'2I 


3'7 


2'94 


2-8 3 


272 


2-62 


2'53 


2'45 


2'37 


2-30 


50 


4-60 


4*32 


4-08 


3'86 


3-66 


3-48 


3*33 


3'i8 


3*05 


2'93 


2-82 


272 


2-63 


2'54 


2- 4 6 


2- 3 8 


5i 


477 


4-48 


4-22 


4-00 


379 


3'6i 


3'45 


3-30 


3'i6 


3^4 


2-92 


2-82 


272 


2-6 3 


2'55 


2-47 


52 


4'95 


4 -6 4 


4-38 


4-14 


3'93 


374 


3'57 


3'4 2 


3-28 


3 -I 5 


3'3 


2-92 


2-82 


273 


2-64 


2-56 


53 


5-i3 


4-81 


4'54 


4-29 


4-08 


3-88 


370 


3'54 


3*4 


3-26 


3'14 


3^3 


2'92 


2-8 3 


274 


2-6 5 


54 


5-32 


4 '99 


4-71 


4'54 


4'23 


4*02 


3-84 


3-67 


3'52 


3-38 


3-26 


3-I4 


3-03 


2-93 


2-84 


275 


55 


5-52 


5-xS 


4-88 


4-62 


4'39 


4-18 


3'99 


3'8i 


3'66 


3'5i 


3-38 


3-26 


3'15 


3'04 


2'95 


2-86 


56 


573 


5-38 


5'07 


4'8o 


4'55 


4'33 


4-14 


3-96 


379 


3-65 


3-5I 


3-38 


3^7 


3-16 


3-06 


2-97 


57 


5'95 


5'59 


5-27 


4-98 


473 


4'5Q 


4-30 


4-11 


3'94 


379 


3^4 


3-5I 


3-39 


3-28 


3-i8 


3-08 


58 


6-18 


5-81 


5'47 


5-18 


4-92 


4-68 


4*47 


4-27 


4-10 


3'93 


379 


3-65 


3'53 


3H 1 


3-30 


3'2o 


59 


6'43 


6-04 


5-69 


5*39 


5'u 


4-87 


4-64 


4'44 


4-26 


4-09 


3'94 


3'8o 


3^7 


3*55 


3'43 


3'33 


60 


6-69 


6-28 


5-92 


5'6i 


5'32 


5'o6 


4-83 


4*62 


4'43 


4-26 


4-10 


3'95 


3-82 


3-69 


3'57 


3'46 


61 


6-97 


6-55 


6-17 


5-84 


5'54 


5-27 


5-03 


4-82 


4-62 


4*44 


4-27 


4-12 


3'97 


3-8 4 


372 


3'6i 


62 


7-27 


6-82 


6-43 


6-09 


578 


5-50 


5'25 


5-02 


4-81 


4-62 


4'45 


4-29 


4-14 


4-01 


3-88 


376 


63 


7-58 


7-12 


6-71 


6-35 


6-03 


574 


5H8 


5'24 


5'02 


4-83 


4-64 


4H8 


4'32 


4-18 


4'5 


3'93 


64 


7-92 


7'44 


7-01 


6-63 


6*30 


5*99 


572 


5'47 


5'25 


5-04 


4-85 


4-68 


4'52 


4'37 


4'23 


4-10 


65 


8-29 


778 


7'33 


6-94 


6'59 


6-27 


5'98 


572 


5'49 


5-27 


5-07 


4-89 


472 


4'57 


4-42 


4-29 


66 


8-68 


8-15 


7-68 


7-27 


6-90 


6-57 


6-27 


6*00 


575 


5-52 


5'3i 


5-12 


4'95 


478 


4-63 


4'49 


67 


9'io 


8-55 


8-06 


7-62 


7-24 


6-89 


6-57 


6-29 


6-03 


579 


5'57 


5'37 


5-i9 


5'02 


4-86 


471 


68 


9'56 


8-98 


8-47 


8-01 


7-60 


7-24 


6-91 


6-61 


6-33 


6-09 


5-86 


5-65 


5'45 


5-27 


5'" 


4'95 


69 


IO'I 


9'45 


8-91 


8-43 


8-00 


7-62 


7-27 


6'95 


6-67 


6-40 


6-16 


5'94 


574 


5'55 


5'37 


5-21 


70 


iO'6 


9*97 


9-40 


8-89 


8-44 


8-03 


7-67 


7'33 


7'03 


675 


6-50 


6-27 


6-05 


5-85 


5-67 


5'49 


7 1 


II'2 


10-5 


9'93 


9-40 


8-92 


8'49 


8-10 


775 


7'43 


7'i4 


6-87 


6-63 


6*40 


6'ig 


5'99 


5'8i 


72 


11-9 


IX '2 


10-5 


9-96 


9'45 


9-00 


8-59 


8-22 


7-88 


7-57 


7-28 


7-02 


678 


6-56 


6-35 


6-16 


73 


I2'6 


11-9 


ii*2 


io - 6 


IO'O 


9'56 


9'i3 


873 


8-37 


8-04 


774 


7-46 


7'2O 


6-97 


675 


6-54 


74 


i3'5 


127 


11-9 


ii'3 


10-7 


10-2 


973 


9*3i 


8*93 


8-57 


8-25 


7-96 


7-68 


7*43 


7-19 


6-97 


75 


14-4 


i3'5 


12-8 


I2'I 


ii'5 


I0'9 


10-4 


9-96 


9'55 


9-18 


8-83 


8-51 


8-22 


7'95 


770 


7-46 


76 


I5-5 


14-6 


137 


T3-0 


12-3 


117 


II'2 


107 


10-3 


9-86 


9*49 


9'i5 


8-8 3 


8-54 


8-27 


8-02 


77 


16-7 


157 


14-8 


I 4 -0 


I3-3 


127 


I2'I 


ir6 


n-i 


10-6 


IO'2 


9-88 


9'54 


9-23 


8-93 


8-66 


78 


18-2 


17-1 


16-1 


I5-2 


X 4'5 


13-8 


I 3 -I 


I2'6 


I2'O 


n-6 


II'I 


107 


10-4 


IO'O 


97 


9-41 


79 


19-9 


18-7 


17-6 


16-6 


15-8 


I5-0 


14-4 


137 


13-2 


I2'6 


12*2 


117 


ii'3 


II'O 


io-6 


10-3 


80 


21-9 


2O'6 


19-4 


18-4 


17-4 


16-6 


15-8 


15-1 


H'5 


I3-9 


I3'4 


12-9 


12-5 


I2'I 


117 


ix3 


81 


24-4 


22-9 


21-6 


20-4 


19-4 


i8'5 


I 7 '6 


16-9 


16-2 


I5-5 


14-9 


14-4 


I3-9 


I3'4 


13-0 


I2'6 


82 


27*5 


25-8 


24'3 


23-0 


21-9 


20-8 


I9-9 


19-0 


18-2 


I7'5 


16-8 


16-2 


157 


15-2 


r 47 


14-2 


83 


31*5 


29-5 


27-9 


26-4 


25-0 


23-8 


227 


217 


20-8 


20'O 


i9 ! 3 


18-6 


17-9 


17*3 


16-8 


16-3 


84 


36-8 


34'5 


32-5 


30-8 


29-2 


27-8 


26-5 


25-4 


24-4 


23H 


22-5 


217 


2I'O 


20'3 


19-6 


19-0 


85 


44-2 


4i'5 


39'i 


37*o 


35-i 


33'4 


31-9 


30-5 


29-3 


28-1 


27-0 


26-1 


25-2 


24'3 


23-6 


22'9 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 


52 


48 


44 


4 o 


16 


3 2 


28 


24 


20 


16 


12 


8 


4 


oo 




llHrs 


10 HOURS. 



Table B. 

Always name the factors taken from Table B the same as the name of declination . 








2 HOURS. 


8 Hrs. 


1 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


tn. 


m. 


m. 


i 

Q 


00 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 


o 
30 




















i 

go 


88 


i 
86 


85 


83 


82 


i;*5 


I'I2 


1-09 


I -06 


1-03 


I'OI 


98, -96 


'94 


92 


31 


I'2O 


I-I7 


1-13 i'io 


1-07 


I'05 


1-02; I '00 


98 


'95 


'93 


92 


90 


88 


86 


85 


32 


1-25 


1*21 


1-18 


1-15 


ri2 


I-og 


I -06 


1-04 


I'OI 


*99 


97 


'95 


'93 


92 


90 


88 


33 


I- 3 


1-26 


1-23 


1-19 


ri6 


I-I3 


I-IO 


I -08 


1-05 


I-0 3 


I'OI 


99 


97 


'95 


'93 


92 


34 


I'35 


1-3,1 


1-27 


1-24 


I'2I 


i'i8 


I-I5 


I' 12 


I'lO 


1-07 


1-05 


1-03 


I 01 


99 


'97 


95 


35 


I- 4 


1-36 


1-32 


1-29 


1-25 


1-22 


rig 


I'l6 


I'M 


I'll 


09 


1-07 


1-05 


1-03 


I'OI 


'99 


36 


!'45 


1-41 


i*37 


1*33 


1-30 


1-27 


1-24 


1*21 


1-18 


1-15 


!3 


i'ii 


1-09 


1-07 


1-05 


03 


37 


i'5i 


1-46 


1-42 


1-38 


i'35 


I-3I 


1-28 1-25 


I'22 


I'20 


17 


i'i5 


1-30 


I'lO 


1-08 


07 


38 


1-56 


1-52 


1-47 


i'43 


1-40 


1-36 


1-33' 1-30 


1-27 


1-24 


'22 


rig 


1-17 


1*15 


I'I2 


10 


39 


1-62 


i'57 


i*53 


i '49 


J'45 


I- 4 I 


1-38 


I'35 


1-32 


I'29 


'26 


1-23 


I'2I 


1-19 


I-I7 


15 


40 


1-68 


1-63 


1-58 


1*54 


1-50 


I- 4 6 


i'43 


i*39 


I- 3 6 


i'33 


31 


1-28 


1-25 


1-23 


I'2I 


19 


4 1 


1-74 


1-69 


1-64 


i -60 


i'55 


1-52 


48 1-44 


I- 4 I 


1-38 


35 


i'33 


I-30 


1-27 


1-25 


23 


42 


1-80 


i'75 


70 


1-65 


1-61 


i '57 


53 1*50 


1*46 


i'43 


40 


i'37 


I'35 


1-32 


I-30 


27 


43 


1-87 


i-Si 


76 


171 


1-67 


1-63 


59 i'55 


51 


1-48 


'45 


1-42 


I'39 


i'37 


i*34 


32 


44 


i'93 


1-87 


82 


177 


173 


1-68 


64 i '60 


'57 


i '53 


50 


i -47 


1-44 


1-42 


i'39 


'37 


45 


2'OO 


1-94 


89 


1-84 


179 


174 


70 


1-66 


62 


i'59 


56 


1-52 


I'49 


1-47 


1-44 


'4 1 


46 


2-07 


2'OI 


'95 


1*90 


1-85 


1-81 


76 


172 


68 


1-65 


61 


1-58 


i'55 


1-52 


1-49 


46 


47 


2-I 4 


2-08 


2'O2 


i*97 


1-92 


1-87 


82 


1*7* 


74 


170 


67 


1-63 


i -60 


i'57 


i'54 


52 


48 


2'22 


2-16 


2'IO 


2-04 


1-99 


1-94 


89 


1-85 


80 


176 


73 


1-69 


1-66 


1-63 


i -60 


57 


49 


2- 3 


2-23 


2-I 7 


2'II 


2-06 


2'OJ 


96 


I -91 


87 


1-83 


79 


175 


172 


1-69 


1-66 


63 


50 


2- 3 8 


2-3I 


2-25 


2'19 


2-13 


2-08 


2-03 


1-98 


1-94 


1-89 


1-85 


1-82 


178 


175 


172 


69 


5i 


2-47 


2- 4 


2'33 


2-27 


2'2I 


2-15 


2'IO 


2*05 


2-01 


1-96 


1-92 


1-88 


1-85 


1-81 


1-78 


75 


52 


2'56 


2'49 


2-42 


2*35 


2-29 


2-23 


2-18 


2-13 


2'08 


2-03 


1-99 


i'95 


1-91 


1-88 


1-84 


81 


53 


2-6 5 


2- 5 8 


2-50 


2-44 


2'37 


2'3I 


2-26 


2'2I 


2-16 


2-II 


2-06 


2'02 


1-98 


i '95 


1-91 


88 


54 


275 


2-6 7 


2-60 


2'53 


2- 4 6 


2- 4 


2'34 


2'29 


2-2 4 


2'19 


2-14 


2'IO 


2-06 


2'02 


1-98 


i'95 


55 


2-86 


2'77 


270 


2-62 


2'55 


2'49 


2'43 


2'37 


2-32 


2'27 


2'22 


2-18 


2-13 


2'O9 


2-06 


2-02 


56 


2-97 


2-88 


2-80 


272 


2-6 5 


2-58 


2-52 


2- 4 6 


2- 4 I 


2- 3 6 


2-3I 


2-26 


2'22 


2-17 


2-13 


2'IO 


57 


3'o8 


2'99 


2-91 


2-83 


275 


2-68 


2-62 


2- 5 6 


2-50 


2'45 


2 '40 


2'35 


2'30 


2-26 


2*22 


z-iS 


58 


3'2o 


3-11 


3-02 


2-94 


2-86 


279 


272 


2-66 


2'60 


2'54 


2'49 


2-44 


2'39 


2'35 


2- 3 


2-26 


59 


3'33 


3-23 


3-14 


3-06 


2-98 


2-90 


2-83 


277 


270 


2*64 


2'59 


2'54 


2 -49 


2-44 


2-40 


2'35 


60 


3-46 


3'36 


3-27 


3'i8 


3-10 


3-02 


2'95 


2-88 


2-81 


275 


2-6 9 


2-64 


2'59 


2'54 


2-49 


2'45 


61 


3'6i 


3'50 


3-40 


S'3 1 


3-23 


3-15 


3-07 


3-00 


2-93 


2'8 7 


2-8l 


275 


270 


2-65 


2'60 


2-55 


62 


376 


3-65 


3'55 


3'45 


3-36 


3-28 


3-20 


3'i3 


3*05 


2'99 


2'93 


2-87 


2'Sl 


276 


2-71 


2'66 


63 


3'93 


3'8i 


37 


3-60 


3'5i 


3'42 


3'34 


3-26 


3-19 


3-12 


3-05 


2'99 


2-93 


2-88 


2-83 


278 


64 


4-10 


3-98 


3-87 


376 


3-67 


3'57 


3'49 


3'4i 


3-33 


3-26 


3'*9 


3'i3 


3-06 


3-01 


2-95 


2-90 


65 


4-29 


4-16 


4'<>5 


3-94 


3-84 


374 


3-65 


3-56 


3-48 


3'4i 


3'34 


3-27 


3*20 


3'M 


3-09 


3-03 


66 


4'49 


4-36 


4-24 


4-12 


4-02 


3-92 


3-82 


373 


3-65 


3'57 


3'49 


3'4 2 


3-36 


3-29 


3'23 


3-18 


67 


4-71 


4'57 


4*45 


4'33 


4-21 


4-11 


4-01 


3-9i 


3-83 


374 


3-67 


3-5? 


3-52 


3'45 


3'39 


3'33 


68 


4 '95 


4-81 


4-67 


4'54 


4*43 


4'32 


4-21 


4-11 


4-02 


3'93 


3-85 


377 


3-70 


3-63 


3-56 


3*50 


69 


5'2i 


5'06 


4-92 


478 


4-66 


4'54 


4'43 


4*33 


4'23 


4-14 


4'5 


3'97 


3-89 


3-82 


375 


3-68 


70 


5*49 


5'33 


5-18 


5-04 


4-91 


479 


4-67 


4'57 


4-46 


4'37 


4-27 


4-19 


4-11 


4*03 


3-96 


3-89 


7 1 


5'8i 


5*64 


5H8 


5'33 


5-19 


5'o6 | 4-94 


4-83 


472 


4-61 


4*52 


4'43 


4'34 


4-26! 4-18 


4-11 


72 


6-16 


5-98 


5-81 


5-65 


5-50 


5'37i 5-24 


5'ii 


5-00 


4-89 


479 


4-69 


4-60 


4'5i 


4*43 


4'35 


73 


6-54 


6-35 


6-17 


6 - oi 


5-85 


570, 5-56 


5'43 


5-3i 


5'2o 


5-09 


4 '99 


4-89 


4'So 


471 


4-63 


74 


6-97 


677 


6-58 


6-40 


6-24 


6-08 


5'93 


579 


5-66 


5'54 


5'43 


5*32 


5'2i 


5'" 


5-02 


4'93 


75 


7M6 


7'25 


7-04 


6-85 


6-67 


6-51 


6-35 


6-20 


6-06 


5'93 


5'8i 


5-69 


5'5B 


5'47 


5'37 


5-28 


76 


8-02 


779 


7'57 


7-36 


7-17 


6-99 6-82 


6-66 


6- 5 i 


6-37 


6-24 


6-n 


5'99 


5-88 


577 


5-67 


77 


8-66 


8-41 


8-17 


7'95 


775 


7'55 7*37 


7'2oj 7-04 


6-88 


674 


6-60 


6-47 


6'35 6-24 


6-13 


78 


9-41 


9-i3 


8-88 


8-64 


8-41 


8-20 8-00 


7-82 


7-64 


7-48 


7'32 


7-17 


7'3 


6-90 


677 


6-65 


79 


10-3 


9'99 


971 


9'45 


9-20 


8'97 


875 


8-55 


8-36 


8-17 


8-00 


7-84 


7-69 


7'54 


7'4i 


7-28 


80 


11-3 


iro 


107 


10-4 


IO'I 


9-89 


9-65 


9-42 


9-21 


9*oi 


8-82 


8-64 


8-48 


8-32 


8-16 


8'02 


81 


I2'6 


12-3 


11-9 


n-6 


11-3 


ii'o 10-7 


10-5 


10-3 


IO'O 


9-82 


9-62 


9'44 


9-26 9-09 


8-93 


82 


14-2 


13-8 


i3'4 


13-1 


127 


I2- 4 I2'I 


n-8 


n-6 


11-3 


ii'i 


io'8 jio'6 


IO'4 JIO'2 


IO'I 


83 


16-3 


15-8 


!5'4 


15*0 


14-6 


14-2 113-9 


I3-5 


13-2 


12-9 


127 


12-4 


I2'2 


11-9 117 


n-5 


84 


19-0 


18-5 


18-0 


*7'5 


17-0 


l6'6 :l6'2 


15-8 


I5-5 


15-1 


14-8 


I4-5 


I 4 '2 


14-0 13-7 


i3'5 


85 


22-9 


22*2 


21-6 


21'0 


20-4 


19-9 


19-4 


19-0 


18-6 


18-2 


17-8 


!7'4 


I7'I 


16-8 16-5 


16-2 




m. 

oo 


m. 

56 


m. 

52 


m. 

48 


m. 

44 


m. m. 
40 36 


m. 
32 


m. 

28 


m. 

24 


m. 
20 


m. 1 m. 
16 1 12 


m. 
8 


m. I m. 
4 1 o 




lOHrs. 


9 HOURS. 



31 
Table B. 

Always name the factors taken from Table B the same as the name of declination. 



1 




3 HOURS. 


4 Hrs. 


fl 

c 
3 


m. 


m. 


m. m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


1 


00 


4 


8 ! 12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 


o 

30 
31 
32 

33 


82 

85 

88 
92 


80 
84 
8 7 
90 


i 

79 
82 
85 
8g 


78 
Si 

84 
-87 


76 
80 

83 
86 


75 
78 
82 

85 


74 

80 
84 


i 

73 

7 e 

79 
82 


COM M M- 

H COt-n M 


i 

71 

74 
% 


70 

73 
76 

79 


70 
72 


6g 
72 
75 
77 


68 

71 
74 
77 


67 
70 
73 

76 


67 
69 
72 

'75 


34 


'95 


'94 


92 


91 


89 


88 


87 


86 


'84 


'83 


82 


81 




80 


79 


/ ? 

7 8 


35 


'99 


97 


96 


'94 


93 


91 


90 


8g 


88 


87 


85 


84 


'83 


'83 


82 


81 


36 


i '03 


I'OI 


'99 


98 


96 


'95 


'93 


92 


91 


90 


'89 


88 


87 


86 


85 


84 


37 


1-07 


1-05 


1-03 


I'OI 


I'OO 


98 


'97 


96 


94 


'93 


92 


'91 


90 


89 


88 


87 


38 


no 


i '09 


1-07 


1-05 


1-04 


I'O2 


I'OI 


"99 '98 


'97 


'95 


'94 


'93 


92 


91 


90 


39 


i'i5 


1-13 


i'ii 


1-09 


1-07 


I -06 


1-04 


1-031 * 01 


I -00 


99 


98 


'97 


95 


'94 


94 


40 


1-19 


I-I7J 1-15 


1-13 


I'll 


I'lO 


i 08 


i -06 


1-05 


1-04 


i 02 


I'OI 


I -00 


'99 


98 


'97 


4 1 


I'23 


I'2I 


i'ig 


1-17 


1-15 


1-13 


1*13 


rio 


i-og 


1-07 


i -06 


1-05 


I'O/ 


1-03 


I'OI 


I'OO 


42 


1-27 


1-25 


I'2J 


I'2I 


ng 


1-18 


1-16 


n/ 


i 13 




I'lO 


i'og 


I '07 


i -06 


1-05 


1-04 


43 


I-32 


I- 3 


1-28 


I'25 


1-24 


I'22 


I'2O 


I'll 


i 17 


1 *5 


i'i/ 


I'12 


III 


no 


1-09 


i -08 


44 


i'37 


T-34 


1-32 


I-30 


1-28 


1-26 


I'2^ 


1-23 


I'll 


1-19 


1-18 


1-16 


1-15 


1-14 


1-13 




45 


1-41 


I'39 


i -37 


I'35 


i- 33 


I' 3 I 


1-29 


i 27 


1-25 


1-24 


I'22 


I-2I 


1-19 


1-18 


1-17 


1-15 


46 


1-46 


i -44 


1-42 


I'39 


1 37 


i -35 


1-3- 


i 31 


1-30 


1-28 


T-26 


1-25 


l"2~' 


1'22 




I 20 


47 


1-52 


i -49 


1-47 


i -44 


1-42 


1-40 


1-38 


1-36 




i 33 


1-31 


1*29 


1-28 


I'26 


1-25 


1-24 


48 


i'57 


i '54 


1-52 


1-49 


1-47 


i'45 


i - 4~ 


1-41 


i* 35 


i "37 


1-36 


*' 3^ 


I' 3 2 


I'3I 


1*30 


I'28 


49 


1-63 


i -60 


I- 57 


I- 55 


1-52 


1-50 


1-48 


1-46 


1-44 


1-42 


1-40 


i'39 




I- 3 6 


i '34 


i'33 


50 


1-69 


1-66 


1-63 


i -60 


1-58 


1-56 


1-53 


i'5i 


1-49 


1-47 


j- 45 


i -44 


I'42 


I'4I 


i '39 


1-38 


51 


i~75 


1-72 


1-69 


1-66 


1-64 


r6i 


J'59 


I- 57 




i'53 


i 5i 


1-49 


I'47 


I' 4 6 


1 '44 


1-43 


52 


i-8r 


1-78 


175 


1-72 


1-70 


1-67 


1-65 


1-62 


i -60 


1-58 


1-56 




i'53 




1-49 


1-48 


53 


1-88 


1-84 


1-81 


1 79 


1-76 


173 


1-71 


1-68 


i 66 


1-64 


1-62 


i -60 


1-58 


I-56 




1-53 


54 


i'95 


1-91 


1-88 


1-85 


1-82 


1-80 


1-77 


175 


1-72 


1-70 


r68 


1-66 


1-64 


I'62 


1-61 




55 


2-02 


i -99 


i '95 


1-92 


1-89 


r86 


i 84 


i 81 


i 79 


1-77 


i '74 


1-72 


1-70 


1-68 


1-67 


1-65 


56 


2'10 


2-06 


2-03 


i -99 


1-96 


i 94 


1-91 


1-88 


1-86 1-83 


1-81 


i -79 


i -77 


175 


173 


1-71 


57 


2-18 


2-14 


2'II 


2-07 


2-04 


2'01 


198 


i '95 


i'93 


1-90 


1-88 


1-86 


1-84 


1-82 


i -80 


1-78 


58 


2'26 


2'22 


2T9 


2-15 


2'12 


2 'Og 


2 06 


2 03 


2'OO 


198 


i '95 


i'93 


1-91 


1-89 


1-87 


1-85 


59 


2'35 


2-3I 


2-28 


2-24 


2'2I 


2'17 


2-I 4 


2-II 


2'08J 2 06 


2-03 


2 OI 


1-98 


1-96 


1-94 


1-92 


60 


2'45 


2' 4 I 


2'37 


2'33 


2-29 


2'26 


2'2 3 


2-20 


2'17 


2-14 


2-II 


2'09 


2-07 


2*04 


2-02 


2'OO 


61 


2'55 


2'5I 


2*47 


2'43 


2 '39 


2' 3 6 


232 


2'29 


2-26 


2-23 


2'20 


2-18 


2-15 


2-13 


2'IO 


2-08 


62 


2'66 


2'6l 


2'57 


2'53 


2 '49 




2-42 


2'39 


2'35 


2-32 


2' 3 


2-27 


2-24 


2'22 


2-19 




63 


2' 7 8 


273 


2'68 


2-64 


2 60 


2'56 


2'53 


2-49 




2*43 


2- 4 


2'37 


2'34 


2-31 


2'29 


2-27 


64 


2-90 


2-85 


2-80 


2-76 


2-72 


2'68 


2-6 4 


2'60 


2'57 


2'53 


2-50 


2-47 


2-44 


2-42 


2'39 


2'37 


65 


3'03 


2' 9 8 


2 93 


2-89 


2-84 


2-80 


2' 7 6 


272 


2-69 


2-65 


2-62 


2'59 


2-56 


2'53 


2'50 


2-48 


66 


3'i8 


3-12 


3'7 


3-02 


2-98 


2'93 


2-89 


2-85 


2 8l 


2-78 


274 


2-71 


2-68 




2-62 


2'59 


67 


3'33 


3'28 


3'22 


3'i7 


3-12 


3-08 


3'3 


2'99 


2-95 


2-91 


2-88 


2-84 


2'8l 


278 


275 


2-72 


68 


3'5 


3'44 


3'38 


3'33 


3-28 


3-23 


3'i8 


3-I4 


3-10 


3'6 


3-02 


2-99 


2'95 


2-92 


2-89 


2-86 


69 


3-68 


3'62 


3'56 


3-5i 


3'45 


3'4 


3'35 




3-26 


3-22 


3-18 


3'M 


3-11 


3-07 


3*04 


3-01 


70 


3-89 


3-82 


376 


370 


3-64 


3'59 


3'54 


3M9 


3-44 


3-40 


3'35 


3 - 3I 


3-28 


3'24 


3'2I 


3-I7 




4-11 


4-04 


3'97 


3-91 


3-85 


379 


374 


3-69 


3-64 


3'59 




3'50 






3'39 


3'35 


72 


4'35 


4-28 


4'2I 


4-14 


4-08 


4-02 


3-96 


3'9i 


3-85 


3'8o 


376 


371 


3-67 


3-63 


3'59 


3'55 


73 


4*63 


4'55 


4'47 


4-40 


4'33 


4-27 


4-21 


4-15 


4-10 


4-04 


3'99 


3'95 


3-90 


3'86 


3'82 


378 


74 


4'93 


4'85 


477 


4-69 


4-62 


4-55 


4'49 


4'43 


4'37 


4-3I 


4-26 


4 '2I 


4-16 


4-11 


4-07 


4-03 


75 


5'28 


5T9 


5-10 


5-02 


4'95 


4-87 


4-80 


474 


4-67 


4-61 


4-56 


4'50 


4'45 


4-40 


4'35 


4-3 1 


76 


5-67 


5'58 


5-48 


5 '4 


5'3 X 


5-24 


5*16 


5'09 


5'O2 


4-96 


4-90 


4 ;8 4 


478 


473 


4-68 


4*63 


77 


6-13 


6'O2 


5'92 


5'8 3 


574 


5-65 


5'57 


5-50 


5-42 


5'35 


5'29 








5-05 


5-00 


78 
79 


6'6 5 
7-28 


6 -54 


6-43 
7-03 


6'33 
6-92 


6-23 
6-82 


6-14 
6-72 


6-05 
6-62 


5'97 
6-53 


5-89 
6-44 


5-82 
6-36 


6-28 


5-67 

6'2I 


6-13 


5'55 
6-07 


5*49 
6'oo 


5'43 
5'94 


OO 00 OO 
K) M O 


8'02 

8'93 

JO'I 


7-88 
8-78 
9-89 


775 
8-63 

973 


7'63 
8-50 

9'57 


7*5* 

8-37 
9*43 


7-40 
8-24 
9-29 


7-30 
8-12 
9-16 


7-20 
8'0i 
9'03 


7-10 
7-91 
8-91 


7-01 
7-80 
8-80 


6*92 
7-71 
8-69 


6-84 

7-62 
8-58 


676 

7'53 
8-48 


6-69 
7'45 
8'39 


6-62 

7'37 
8-30 


6-55 

7-29 

8-22 


83 


"'5 


11-3 


ii'i 


I'O 


io-8 


io - 6 


10-5 10-3 


IO'2 


IO'I 


9'94 


9-82 


971 


9-60 


9'50 


9-40 


84 


i3'5 


13-2 


13-0 


2'8 


I2'6 


12-4 


I2'2 12*1 


11*9 


n*8 


ii'6 


ii*5 


ii"3 


1*2 


I'l 


I I'O 


85 


16-2 


15-9 


15-6 


15-4 


15-1 


149 


14-7 !i 4 '5 


i4'3 


14-1 


14-0 


3'8 


i3'6 


3'5 


3'3 


13-2 




m. 


m. 1 m. | m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 | 52 i 48 


44 


40 


36 


3 2 


28 


2 4 


20 


16 


12 


8 


4 


oo 




9 Hrs. 


8 HOURS. 



32 
Table B. 

Always name the factors taken from Table B the same as the name of declination. 



1 


4 HOURS. 


5 Hrs. 


1 


m. 


m. 


m. 


m. 


m. 


rn. 


m. 


m. 


m. 


rn. 


111. 


m. 


m. 


m. rn. 


m. 


1 


00 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 56 


00 


o 


/ i 


/ 


t 




| 


t 


/ 


; l 




f 










30 


. -67 -66 


65 


65 


64 


64 


63 


63 


62 


62 


61 


61 


61 


60 


60 


60 


31 


69 -69 


68 


67 


67 


66 


66 


65 


65 


64 


64 


. '64 


63 


63 


63 


62 


32 


72 71 


71 


70 


70 


69 


68 


68 


67 


6 7 


66 


66 


66 


65 


65 


65 


33 


75 '74 


'74 


'73 


72 


72 


7i 


71 


70 


70 


69 


69 


68 


68 


68 


6 7 


34 


78 


77 


76 


7 6 


75 


74 


74 


73 


73 


72 


72 


71 


7i 


7i 


70 


7 


35 


81 


80 

8- 


79 


79 


78 

. O 


' 


'I 7 


76 


'1 


75 


75 


74 


74 


73 


73 


72 


36 


534 


- 


2 


o2 


01 


'oO 


oO 


79 


7 8 


7 8 


77 


77 


76 


76 


76 


75 


37 


87 


86 


85 


'85 


84 


'S3 


82 


82 


81 


81 


80 


80 


79 


79 


78 


78 


38 


90 


89 


88 


88 


87 


86 


86 


85 


84 


84 


83 


83 


82 


82 


81 


81 


39 


'94 


'93 


92 


91 


90 


89 


89 


88 


87 


87 


86 


86 


'85 


'85 


84 


84 


40 


'97 


96 


95 


'94 


'93 


93 


92 


91 


90 


90 


89 


89 


88 


88 


87 


87 


4i 


I -00 


99 


98 


98 


97 


96 


'95 


'94 


'94 


93 


93 


92 


91 


91 


90 


90 


42 


1-04 


03 


02 


I'OI 


I'OO 


'99 


99 


98 


'97 


96 


96 


'95 


'95 


'94 


'94 


'93 


43 


i -08 


07 


06 


1*05 


1-04 


1-03 


02 


I'OI 


I'OI 


I'OO 


99 


99 


98 


98 


97 


'97 


44 


I'M 


10 


09 


i -08 


1-07 


1-07 


06 


1-05 


1-04 


1-03 


1*03 


I'O2 


I'02 


I'OI 


I -00 


I -00 


45 


1*15 


14 


13 


I' 12 


i'ii 


I'lO 


09 


1-09 


i -08 


1-07 


i -06 


I -06 


I'O5 


1-05 


1-04 


1-04 


46 


I'2O 


18 


17 


1-16 


i'i5 


1-14 


13 


I'I2 


I'I2 


i'ii 


I'lO 


I'lO 


I-09 


i -08 


i -08 


1-07 


47 


1-24 


"23 


21 


1-20 


1-19 


1-18 


17 


1-16 


1-16 


1-15 


1-14 


I'I3 


I'll 


I'I2 


I'I2 


i'ii 


48 


1-28 


27 


26 


I'25 


1-24 


1*23 


22 


I'2I 


I'2O 


1-19 


1-18 


I-I7 


I-I7 


1-16 


ri6 


1*15 


49 


i'33 


32 


3 


I'29 


1-28 


1-27 


26 


I-2 5 


I'24 


1-23 


I'22 


I '22 


1*21 


I'2O 


I'20 


1-19 


5* 


1-38 


36 


'35 


i'34 


i '33 


1-31 


3 


1-29 


I'29 


1-28 


27 


1-26 


1-25 


I'25 


I-2 4 


1-23 


5i 


1-43 


"4 1 


4 


i'39 


!'37 


1-36 


'35 


I'34 


I'33 


1-32 


'3 1 


I' 3 I 


I- 3 


1-29 


1-28 


1-28 


52 


1-48 


46 


'45 


1-44 


1-42 


1-41 


4 


I'39 


I- 3 8 


I- 37 


36 


i'35 


I'35 


I'34 


I'33 


i'33 


53 


i'53 


52 


'SO 


i'49 


1-48 


1-46 


'45 


i -44 


I'43 


1-42 


41 


1-40 


I- 4 


I'39 


I- 3 8 


i'37 


54 


i'59 


57 


56 


1 '54 


i'53 


1-52 


'SI 


1-50 


i -48 


!'47 


46 


1-46 


i '45 


I- 44 


I'43 


1-42 


55 


1-65 


"63 


I'62 


i -60 


i '59 


1-58 


56 


i'55 


!'54 


i'53 


52 


i'5i 


1-50 


I'49 


I'49 


1-48 


56 


1-71 


70 


1-68 


r66 


1-65 


1-64 


62 


1-61 


i -60 


i'59 


58 


i'57 


1-56 


I'55 


I'54 


i'53 




178 


76 


1-74 


173 


1-71 


1-70 


6 9 


i -67 


1-66 


1-65 


64 


1-63 


1-62 


1-61 


I 60 


i'59 


58 


1-85 


83 


1-81 


i -80 


1-78 


1-77 


75 


1-74 


173 


171 


170 


1-69 


1-68 


1-67 


1-66 


1-66 


59 


1-92 


90 


1-88 


1-87 


1-85 


1-84 


82 


1-81 


1-79 


1-78 


177 


1-76 


175 


1-74 


'73 


1-72 


60 


2'OO 


1-98 


1-96 


1-94 


i'93 


1-91 


90 


1-88 


1-87 


1-86 


1-84 


1-83 


1-82 


1-81 


i -80 


i -79 


61 


2'08 


2-06 


2-04 


2'O2 


2'OI 


1-99 


97 


1-96 


i'95 


i '93 


1-92 


1-91 


1-90 


1-89 


1-88 


1-87 


62 


2T7 


2-15 


2-13 


2'II 


2-09 


2-08 


2 p o6 


2*04 


2-03 


2'OI 


2 00 


1-99 


1-98 


1-97 


i 96 


i'95 


63 


2-27 


2-24 


2'22 


2'2O 


2-18 


2-17 


2-15 


2-13 


2'12 


2'IO 


20 9 


2-08 


2-06 


2-05 


2-04 


2-03 


64 


2'37 


2'34 


2-32 


2'30 


2-28 


2-26 


2-24 


2-23 


2'2I 


2'2O 


2'l8 


2-17 


2'l6 


2-14 


2-13 


2'12 


65 


2-48 


2'45 


2'43 


2-41 


2'39 


2'37 


2'35 


2'33 


2'3I 


2-30 


2-28 


2-27 


2-25 


2-24 


2-23 


2'22 


66 


2'59 


2'57 


2'54 


2-52 


2-50 


2-48 


2-46 


2'44 


2-42 


2-41 


2-39 


2-38 


2-36 


2'35 


2'34 


2'33 


67 
68 


2-72 
2-86 


2-69 
2-83 


2-6 7 
2'8o 


2'6 4 
2- 7 8 


2-62 
275 


2 '60 
273 


2-58 
2-71 


2-56 
2-69 


2'54 
2-6 7 


2-52 
265 


2-51 

2-63 


2'49 
2-62 


2-48 

2'6o 


2-46 
2'59 


2'45 
2'57 


2'44 
2' 5 6 


69 


3-01 


2-98 


2'95 


2'92 


2-90 


2'8 7 


2-85 


2-83 


2'8l 


279 


277 


2-76 


274 


272 


271 


2'7O 


70 


3'i7 


3'M 


3-11 


3'08 


3-06 


3-03 


3-01 


2-98 


2-96 


2'94 


2-92 


2-91 


2-89 


2-87 


2-86 


2-84 


7 1 


3'35 


3-32 


3-29 


3-26 


3'23 


3 -20 


3'i8 


3'i6 


3-I3 


3 -II 


3-09 


3'07 


3'05 


3-04 


3-02 


3'01 


72 


3'55 


3-52 


3 '49 


3'45 


3'4 2 


3'4 


3'37 


3'34 


3-32 


3-30 


3-28 


3-26 


3'24 


3-22 


3'20 


3'i9 


73 


378 


374 


370 


3-67 


3-64 


3'6i 


3-58 


3'55 


3'53 


3-50 


3-48 


3H6 


3'44 


3'4 2 


3'40 


3*39 


74 


4'03 


3'99 


3'95 


3'9i 


3'88 


3-85 


3-82 


379 


376 


374 


37 1 


3-69 


3-6 7 


3-65 


3'63 


3'6i 


75 


431 


4-27 


4'23 


4-19 


4^5 


4-12 


4-09 


4-05 


4'3 


4-00 


3'97 


3'95 


3-92 


3-90 


3-88 


3-86 


76 


4-63 


4'59 


4'54 


4 '50 


4-46 


4'43 


4'39 


4'3 6 


4'33 


4'30 


4-27 


4-24 


4-22 


4-19 


4-17 


4^5 


77 


5-00 


4'95 


4-91 


4-86 


4-82 


478 


474 


471 


4'6 7 


4-64 


4-61 


4'58 


4'55 


4'53 


4'5i 


4-48 


78 


5*43 


5-33 


5'33 


5-28 


5'23 


5'i9 


5'*5 


5'ii 


S-o? 


5-04 


5'oi 


4-98 


4'95 


4-92 


4-89 


4-87 


79 


5-94 


5-88 


5-83 


577 


572 


5-68 


5-63 


5'59 


5'55 


5'5i 


5'47 


5'44 


SHI 


5'38 


5'35 


5'33 


80 


6'55 


6-48 


6-42 


6-37 


6-31 


6-26 


6-21 


6-16 


6-12 


6-07 


6-04 


6-00 


5-96 


5*93 


5'90 


5-87 


Si , 


7-29 


7-22 


7-I5 


7-09 


7-02 


6-97 


6*91 


6-86 


6'8i 


6-76 


6-72 


6-68 


6'6 4 


6-60 


6'57 


6'54 


82 ' 


8-22 


8-14 


8-06 


7'99 


7-92 


7-85 


779 


773' 7 <6 7 


7-62 


7'57 


7'53 


7-48 


7'44 


7-40 


7'37 


83 


9-40 


9'3 J 


9-22 


9-14 


9*06 


8-99 


S'92 


8-85 1 8-78 


8-72 


8-67 


8-61 


8-56 


8-52 


8-47 


8-43 


84 


II'O 


10-9 


10-8 


10-7 


10-6 


10-5 


io'4 


10-3 io - 3 


I0'2 


IO'I 


IO'I 


IO'O 


9'95 


9-90 


9-85 


85 


13-2 


13-1 


12-9 


12-8 


127 


I2'6 


12-5 


12-4 12-3 


I2'2 


I2'2 


I2'I 


I2'0 


I2'0 


11-9 


ii-8 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




oo 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


oo 




8 lira. 


7 HOURS. 



33 
Table B. 

Always, name the factors taken from Table B the same as the name of declination. 



c 

1 


5 HOURS. 


6Hrs. 


1 


m. 


m. 


m. m. 


in. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


1 


00 


4 


8 12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


00 




30 


oo -60 


1 
'59 '59 


'59 


'59 


5* 


58 


58 


58 


58 


58 


58 


58 


58 


58 


3 1 


62 


62! '62 


61 


61 


61 


61 


61 


61 


60 


60 


60 


60 


60 


60 


'60 


32 


65 


6 4 | "64 


64 


64 


63 


63 


63 


63 


63 


63 


63 


63 


63 


62 


62 


33 


6 7 | -6 7 | -67 


66 


66 


66 


66 


66 -65 


65 


65 


65 


65 


65 


65 


'65 


34 


70j -70 '69 


69 


69 


68 


68 


68; -68 


68 


68 


68 


68 


67 


67 


67 


35 


72; 72 72 


72 


71 


-7.1 


7* 


71 


71 


70 


70 


7 


70 


70 


70 


70 


36 


75 


'75 '75 


'74 


'74 


74 


74 


73 


73 


73 


73 


73 


73 


73 


73 


73 


37 


78 


7 8 


77 


'77 


77 


77 


76 


76 -76 


76 


76 


76 


75 


75 


75 


75 


38 


81 


81 


80 


80 


80 


79 


79 


79 79 


79 


78 


78 


78 


78 


78 


ft 


39 


84 


83 


8 3 


83 


82 


82 


82 


82 -82 


81 


81 


81 


81 


81 


81 


81 


40 


87 


86 


86 


86 


85 


'85 


85 


85J '85 


84 


84 


84 


84 


84 


84 


84 


4i 


90 


90 


89 


89 


89 


88 


88 


88 


88 


87 


87 


87! -87 


87 


87 


87 


42 


'93 


93 


92 


92 


92 


91 


91 


91 


91 


91 


90 


90 -90 


90 


90 


90 


43 


97 


96 


96 


'95 


'95 


95 


'94 


'94 


'94 


'94 


'94 


'93 


'93 


'93 


'93 


'93 


44 


I'OO 


I'OO 


'99 


99 


98 


98 


98 


98 


97 


97 


'97 


97 


97 


'97 


'97 


97 


45 


1-04 


1-03 


1-03 


I'02 


1-02 


I'02 


oi 


I'OI 


I -01 


I'OI 


I'OO 


I'OO 


I'OO 


oo 


I'OO 


I'OO 


46 


1-07 


1-07 


i -06 


I -06 


1-05 


1-05 


05 


1-05 


1-04 


04 


1-04 


i '04 


i '04 


04 


1-04 


i -04 


47 


I'll 


I'll 


I'lO 


i-ioj 1-09 


1-09 


09 


i -08 


i -08 


08 


i-oS 


1-07 


1-07 


07 


07 


1-07 


48 


1-15 


1-14 


1-14 


I'M 


I-I3 


I'I 3 


12 


i*ia 


I'I2 


12 


I'll 


i'ii 


I'll 


ii 


ii 


i'ii 


49 


rig 


1-19 


1-18 


rx8 


I-I7 


I-I7 


16 


1-16 


rtf 


16 


1 * I 5 


IfI 5 


f.M 


15 


15 


1-15 


5 


1-23 


1-23 


1-22 


I'22 


I'2I 


I'2I 


21 


I'2O 


1-20 


20 


I'20 


rig 


rig 


19 


i9 


1-19 


51 


1-28 


1-27 


1-27 


1-26! 1-26 


1-25 


25 


1-25 


I-2 4 


24 


1-24 


1-24 


1-24 


24 


24 


1-23 


52 


i'33 


1-32 


I-3I 


1-31 


I' 3 


I-30 


3 


1-29 


1-29 


29 


1-28 


1-28 


1-28 


28 


28 


1-28 


53 


I- 37 


i'37 


1-36 


I- 3 6 


I'35 


i'35 


J '34 


i'34 


I'34 


'33 


1-33 


i'33 


i '33 


'33 


'33 


i'33 


54 


1-42 


1-42 


I- 4 1 


I-4I 


I-40 


1*40 


i'39 


i'39 


I'39 


3 8 


1-38 


1-38 


1-38 


38 


38 


1-38 


55 


1-48 


1-47 


I'47 


I- 4 6 


I 45 


i '45 


i'45 


1-44 


1-44 


'44 


i'43 


1 43 


I> 43 


'43 


'43 


i '43 


56 


i '53 


i'53 


I-52 


1-52 


i*5* 


I'S* 


1-50 


1-50 1-49 


'49 


1-49 


i -49 


1-48 


48 


48 


1-48 


57 


i'59 


i'59 


1-58 


I'57 


i'57 


1-56 


1-56 


i'55 


i '55 


55 


i'55 


i-54 


i'54 


'54 


'54 


I- 54 


58 


1-66 


1-65 


I-6 4 


I-6 4 


1-63 


1-63 


1-62 


1-62 


1-61 


61 


1-61 


i -60 


i -60 


60 


60 


i -60 


59 


1-72 


1-72 


171 


I-70 


1-70 


1-69 


1-69 


1-68 


1-68 


67 


1-67 


1-67 


1-67 


67 


66 


1-66 


60 


1-79 


1-79 


I' 7 8 


I'77 


1-76 


1-76 


175 


175 


175 


74 


i -74 


i -74 


173 


73 


73 


173 


61 


1-87 


1-86 


I-8 5 


1-84! 1-84 


1-83 


1-83 


1-82 


1-82 


81 


r8i 


1-81 


1-81 


81 


80 


i -80 


62 


i'95 


1-94 


I'93 


1-92 


1*92 


1-91 


1-90 


1-90 


1-89 


89 


1-89 


1-89 


1-88 


88 


1-88 


1-88 


63 


2-03 


2'O2 


2'OI 


2'OI 


2.00 


1-99 


1-99 


1-98 


1-98 


97 


i -97 


1-97 


i -97 


96 


1-96 


i -96 


64 


2'12 


2-II 


2'IO 


2'IO 


2-09 


2-08 


2-08 


2-07 


2*07 


2-06 


2-06 


2-06 


2-05 


2-05 


2*05 


2-05 


65 


2'22 


2'2I 


2'2O 


2-19 


2-18 


2-18 


2-17 


2-17 


2-16 


2-16 


2-15 


2-15 


2-15 


2-15 


2-14 


2-14 


66 


2'33 


2-3I 


2- 3 I 


2-30 


2-29 


2-28 


2-27 


2-27 


2-26 


2-26 


2-25 


2-25 


2-25 


2-25 


2-25 


2-25 


67 


2-44 


2'43 


2-42 


2-41 


2-40 


2-39 


2-39 


2-38 


2'37 


2'37 


2-36 


2-36 


2-36 


2-36 


2-36 


2-36 


68 
69 


2-56 
270 


2-55 

2-68 


2'54 
2-67 


2'53 

2-66 


2-52 
2-6 5 


2-51 
2-65 


2-51 
2-64 


2-50 
2-63 


2-49 
2-62 


2-49 
2-62 


2-48 
2-62 


2-48 
2-61 


2-48 

2'6l 


2-48 

2'6l 


2-48 

2'6l 


2-48 

2'6l 


7 


2-8 4 


2-83 


2-82 


2-8i 


2-80 


279 


2-78 


277 


277 


2-76 


276 


275 


275 


275 


275 


275 


71 


3'01 


2-99 


2-98 


2'97 


2^96 


2'95 


2-94 


2'93 


2'93 


2-92 


2-92 


2-91 


2-91 


2-91 


2-90 


2-90 


72 
73 


3 -I 9 
3'39 


3-I7 
3'37 


3-6 
3'36 


3-15 
3'34 


3'i4 
3'33 


3'i3 
3-32 


3-12 
3'3i 


3-11 
3'3<> 


3-10 
3-30 


3-09 
3-29 


3-09 
3-28 


3-09 
3-28 


3-08 3-08 
3-28 3-27 


3-08 
3'27 


3'o8 
3-27 


74 


3'6i 


3'59 


3-58 


3'57 


3'55 


3'54 


3'53 


3-52 


3'5i 


3'5i 


3*50 


3*50 


3'49 


3'49 


3'49 


3'49 


75 


3-86 


3-85 


3-83 


3'82 


3-80 


379 


378 


377 


3-76 


375 


375 


374 


374 


373 


373 


373 


76 


4'!5 


4*13 


4-12 


4-10 


4-09 


4-07 


4-06 4-05 


4-04 


4'03 


4-03 


4-02 


4-02 


4-01 


4-01 


4-01 


77 


4-48; 4H6 


4'45 


4'43 


4-41 


4-40 


4'39 4'37 


4-36 


4-36 


4'35 


4'34 


4'34 


4'33 


4'33 


4'33 


78 


4-87 


4-85 


4-83 


4-81 


479 


478 


4-76 


475 


474 


473 


472 


472 


47i 


4-71 


471 


470 


/ 

79 


5-33 


5-30 


5-28 


5-26 


5'24 


5'22 


5'2i 


5'20 


5-18 


5'i7 


5'i6 


5'i6 


5-15 


5-I5 


5'i5 


5-I4 


80 


5-87 


5-84 


5-82 


5-8o 


578 


576 


574 573 


57i 


5*70 


5-69 


5*69 


5-68 


5-67 


5-67 


5-67 


81 


6'54 


6-51 


6-48 


6'45 


6-43 


6- 4 T 


6-39 6-38 


6-36 


6-35 


6-34 


6-33 


6-32 


6-32 


6-31 


6-31 


82 


7'37i 7'33 


7'3 


7*27 


7' 2 5 


7'23 


7-20 7-19 


7-17 


7-I5 


7-14 


7' J 3 


7'*3 


7-12 


7-12 


7-12 


83 


8-43 8-39 


8-36 


8-33 


8-30 


8-27 


8-25 8-22 


8-21 


8-19 


8-18 


8-16 


8-16 


8-15 


8-15 


8-14 


W O 

84 


9-85^ q-8i 


9-76 


9'73 


9-69 


9-66 


9-63 9-61 


9' 59 


9'57 


9'55 


9*54 


9'53 


9-52 


9'52 


9-5i 


T 

85 


11-83 


11-78 


ii'73 


11-69 


11-64 


11-61 


"'57 "'54 


11-52 


11-49 


11-47 


1 1 '46 


"45 


11-44 


"'43 


ii'43 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


nT 




oo 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


00 




7Hrs. 


6 HOURS. 



3 Azimuth. 



34 
Table A. 

When hour angle is less than 6 hours, name the factors taken from Table A contrary to name of lat. 





HOUR. 


2 


m. 


m. 


m. ! m. 


m. 


m. m. 


m. 


m. 


m. 1 m. m. 


m. m. 


m. 


m. 




1 


4 


8 I 12 16 


20 24 28 32 


36 1 40 44 


48 52 


56 


60 


85 












& 


109 


93-1 81-3 72-2 






42-7 


2620 


655 


327! 218 


163 


64-8 58-8 53-8 49-5 


4V8 


8 5 J 


2912 


728 


364 243 


182 


*45 


121 


104 


90-4 


80-2 


72-1 65-4 


59-8 55-0 


51-0 


47'4 


86 


3277 


819 


410 273 


205 


164 136 


117 


1 02 


90-3 


81-1 


73-6 


67-3 


62-0 


57'4 


53'4 


86 


3747 


937 


468 


312 


234 


187! 156 


133 


116 103 


92-7 


84-1 


76-9 


70-8 


65-6 


61-0 


8? 


4373 


1093 


546 


364 


273 


218 


182 


155 


136 121 


108 


98-2 


89-8 


82-6 


76-5 


71-2 


87* 


5259 


1312 


656 


437 


328 


262 


218 


187 


163 145 


130 


118 108 


99-2 


91-9 


85-5 


88 


6563 


1641 


820 


546 


410 


327 


273 


233 


204 181 


162 


J 47 135 


124 


H5 


107 


88 


8752 


21881094 


729 


546 


436 363 


311 


272 241 


217 


196 


180 


165 


153 


T 43 


89 
39| 


13129 
26261 


3282 1641 
65653281 


1093 
2186 


819 
1639 


655: 545467 4 8 362 
13101090,933 1815 723 


325 
650 


295 
590 


270 
539 


248 230 
496 [460 


214 

428 




m. 


m. 


m. 


m. 


m. 


m. m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. m. 


m. 




59 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 







11 HOURS. 





1 HOUR. 


5 


m. m. 


m. 


m. ! m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




4 


8 


12 ! 16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 




























8 5 


42-7 39-9 


37'4 


35-2 


33-2 


31-4 


29-8 


28-3 


26-9 


25-7 


24-5 


23-4 


22-4 


21-5 


20-6 


19-8 




47'4 44-3 


41-6 


39-1 




34-9 


33-1 




29-9 


28-5 


27-2 


26-1 


24-9 


23-9 


22-9 


22-O 


86 


53'4 49-9 


46-8J 44-0 


4i-5 


39-3 


37'3 


35'4 


33-7 32-1 


30-7 


29-3128-1 


26-9 


25-8 


24-8 


86 


61-0 57-0 


53-5 


5'3 47-5 


44-9 


42-6 


4'5 


38-5 


30-7 


35-i 


33'5j32-i 


30-7 


29-5 


28-3 


' 8 7 


71-2 66-5! 62-4 


58-7 


55'4 


52-4 


49-7 


47-2 


45-o 


42-9 


40-9 


39-i 


37-4 


35-9 


34'4 


33' 


87* 


85-5! 79-9 74-9 7'5 


66-5 


62-9 


59-7 


56-7 


54' 




49-1 


47-0 








39-7 


88 


107 


99-9 93-7 88-1 


83-2 


78-7 


74-6 


70-9 


67-5 


64-3 


6!- 4 


58-7 


56-2 


53-9 


51-7 


49-6 


88 


I43 


133 


125 1x8 


in 


i5 


99-5 


94-5 


90-0 


85-8 


81-9 


78-3 


74-9 


71-8 


68-9 


66-1 


.. .89 


214 


200 


187 


176 166 


157 


149 142 


135 


129 


123 117 


112 


108 


103 


99-2 




428 


4 00 


375 


353 333 


315 


299 284 


270 J257 


246 235 


225 


216 


207 


198 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


in. 


m. 


m. 


m. 




60 


56 52 


48 


44 


4 


36 


32 


28 


24 


20 


16 


12 8 


4 







10 HOURS. 







2 HOURS. 


,1 


m. m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. m. 


m. 


m. 


m. 


m. 


m. 


m. 




4 


8 


12 


16 


20 1 24 


28 


32 6 


40 


44 


48 


52 


56 


60 


85 


19-8 


19-0 18-3 


17-6 16-9 


16-3 


/ 
15-7 












ii-4 


15-2 14-6 14-1 


13-6 13-1! 12-7 


12-3 


n-8 


85* 


22-O 


2I-I 20-3 


19-6 18-8 


18-2 17-5 


16 9! 16-3 


15-7 


15-1 


14-6; 14-1 


13-6 13-2 


12-7 


86 


24-8 


23-8 22-9 


22-0 21-2 


20-4 19-7 


19-0 18-3 


17-7 


17-0 


16-5! J 5'9 


I5-3JI4-8 


14-3 


86 


28-3 


2 7 -2 


26-2 


25-2 


24-2 


23-4 


22-5 


21-7 20-9 


2O-2 


19-5 


18-8 


18-2 


17-5, 16-9 


16-3 


87 


33-o 


31-8 


3'5 


29-4 


28-3 


27-3 


26-3 


25-3 24-4 


23-6 


22-7 


22-0 


21-2 


20-5 


19-8 


19-1 


87* 


39-7 


38-1 


36-7J 35-3 


34' 


32-7 


3i-5 


30-4 


29-3 


28-3 


27-3 


26-3 


25-4 


24-6 


23-7 


22-9 


88 


49-6 


47'7 


45'8 


44-1 


42-5 


40-9 


39-4 


38-0 


36-7 


35-4 


34' 1 


329 


3 I-8 30-7 


29-7 


28-6 


88 


66-1 


63-6 


61-1 


58-8 


56-6 


54'5 


52-6 


50-7 


48-9 47-2 


45'5 


43-9 


42-4 


41-0 


39-5 


38-2 


89 


99-2 


95-3 


9i-7 


88-2 


84-9 


81-8 


78-9 76-0 


73-3 70-7 


68-3 


65-9 


63-6 61-4 


59-3 


57-3 


89 


198 


191 


183 


176 


170 


164 


158 152 


147 ,142 


137 


132 


127 123 


119 


H5 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




60 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 4 







9 HOURS. 



When hour angle is more than 6 hours, name the factors taken from Table A the same as the 
name of the latitude. 



35 

Table B. 

Always name the factors taken from Table B the same as the name of declination. 



rt . 


HOURS. 




m. 


m. 


m. m. 


m. 


m. 


m. 


m. i m. 


m. 


m. 


in. 


m. 


m. 


m. 


m. 


& 


\ 4 


8 12 16 


20 


24 


28 i 32 


36 


40 44 i 48 


52 


56 


60 




















/ / i / 






85 


2620 


655 


328 


218 


164 


131! 109 


93-8 


82-1 


73-1 


65-8 


59-9 55' 5'8 


47-2 


44-2 


8.54 


2912 


728 


364 


243 


182 


146 122 


104 




81-2 


73'2 


66-6 61-1 56-5 


52-5 


49-1 


86 


3277 819 


410 


273 


205 


164 137 


H7 


103 


91-4 


82-4 


74-9 68-8 63-6 


59-i 


55'3 


86|- 


3747 


937 


468 


312 


234 


1 88 


156 


134 117 


105 


94'2 


85-7 


78-6 


72-7 


67-6 


63-2 


87 


4373 


1093 


547 


365 


274 


219 183 


157 


137 


122 


no 


IOO 


91-8 


84-8 


78-9 


73'7 


872 


5259 


1312 


656 


438 


328 


263 219 


188 165 


I 4 6 


132 


120 


no 


102 


94-7 


88-5 


88 


6563 


1641 


821 


547 


411 


329 


274 


235 ,206 


183 


165 


150 


138 


127 


118 


in 


884 


8752 


2188 


1094 


730 


547 


438 


365 


313 274 


244 


220 


2OO 


184 


I 7 


158 


148 


89 


13129 


3283 


1642 


1095 


821 


657 


548 


47 1412 


366 


330 


3OO 


276 


25") 


237 


221 


- 89 1 


26261 6566 


3283 


2190 


1643 


1315 


1096 


94 


823 


733 


660 


601 


55i 59 


474 


443 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




59 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


o 




11 HOURS. 






1 HOUR. 


13 -2 


m. 


in. 


in. 


in. 


m.. _ 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. m. 


m. 


Q 





4 


8 


12 


18 


2) 


2* 


28 


32 


36 


40 


44 


48 


52 1 56 


60 




























' 1 ' 




85 


44-2 


4i-5 39-i 


37' 


35-i 


33'4 


3i-9 


3'5 


29-3 


28-1 


27-0 


26-1 


25-2 


24-31 23-6 


22-9 


&>* 


49-1 


4 ( >! 43-5 


41-1 


39-o 


37-2 


35'5 


33-9 


32-5 


31-2 


30-1 


29-0 


28-0 


27-1 


26-2 


25-4 


86 


55'3 


51-9 


48-9 


46-3 


43-9 


41-8 


39-9 


38-2 


36-6 


35-2 


33-8 32-6 


3i'5 


30-5 


29-5 


28-6 


86$ 


63-2 


59-3 


55-9 


52-9 


50-2 


47-8 


45-6 


43-6 


41-8 


40-2 


38-7 


37'3 


36-0 


34-8 


33-7 


32-7 


87 


73-7 


69-2 


65-3 


61-7 


58-6 


55-8 


53-2 


50-9 


48-8 


46-9 


45-i 


43-5 


42-0 


40-6 


39-4 


38-2 


874 


88-5 


83-1 


78-3 


74-1 


70-4 


67-0 


63'9 


61-1 


58-6 


56-3 


54-2 


52-2 


50-4 


48-8 


47-2 


45-8 


.88 


in 


104 


97-9 


92-7 


88-0 


83-7 


79-9 


76-4 


73'3 


70-4 


67-8 


65-3 


63-1 


61-0 


59-1 


57'3 


88 


148 


139 


131 


124 


117 


112 


107 


102 


97'7 


93-9 


90-4 


87-1 


84-1 


81-3 


78-8 


76-4 


__8 9 - 


.221 


208 


196 


185 


176 


168 


160 


153 


147 


141 


136 


131 


126 


122 


118 


H5 


894 


443 |4 l6 


392 


37i 


352 


335 


320 


3 06 


293 


282 


271 


261 


252 


244 


236 


229 




in. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. m. 


m. 


m. 


m. 


m. 




60 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 1 16 


12 


8 


4 


o 





10 HOURS. 



A 


2 HOURS. 


A o 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


in. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


&~ 





4 


8 


12 


16 


20 


24 , 28 


32 


36 


40 


44 


48 


52 


56 


60 


85 












19-9 


19-4 


19-0' 18-6 


18-2 












16-2 


22-9 


22-2 


21-6 


21-0 


20-4 


17-8 


17-4 


17-1 


16-8 


16-5 


8 5 i 


25-4 


24-7 


24-0 


23-3 22-7 


22-2 


21-6 


2I-I 2O-6 


2O-2 


19-8 


19-4 


19-0 


18-6 


18-3 


18-0 


86 


28-6 


2 7 -8 


27-0 


26-3 25-6 


24-9 


24-3 


23-8 


23-2 


22-7 


22-2 


21-8 


21-4 


2I-O 


2O-6 


2O-2 


8.64 


32-7 


31-7 


3'9 


3O-O, 29-2 


28-5 


27-8 


27-2 


26-6 


26-0 


25-4 


24-9 


24-4 


2 4 -0 


23-5 


23-1 


87 


38-2 


37- 


36-0 


35-o 34-i 


33-3 


32-5 


31-7 


31-0 


3'3 


29-7 


29-1 


28-5 


28-0 


27-5 


27-0 


8 7 | 
88 


45-8 
57-3 


44'5 
55-6 


43-2 
54' 


42-1 
52-6 


41-0 
51-2 


39-9 39-o 
49-948-7 


3 8-I 

47-6 


37-2 
46-5 


30-4 
45-5 


35'b 
44-6 


34-9 
43-6 


34-2 
42-8 


33-0 

42-0 


33-o 
41-2 


32-4 

4'5 


88 
89 
89* 


76-4 

H5 
229 


74-1 
in 

222 


72-1 
1 08 
216 


70-1 
i5 

210 


68-3 

102 

205 


66-6 
999 

200 


65-0 
97-5 
195 


63-5 
95-2 
190 


62-0 

93-1 
186 


60-7 
91-0 

182 


59-4 
89-1 

178 


58-2 
87-3 
175 


57-i 
85-6 
171 


56-0 
84-0 
1 68 


55-o 
82-5 
165 


54' 

81-0 
162 





m. 


m. 


m. 


m. 


m. 


in. 


m. 


m. 


m. ; m. 


m. 


m. 


m. 


m. 


m. 


m. 





60 


56 


52 


4 8 


44 


40 


36 


32 


28 | 24 


20 


16 


12 


8 


4 







9 HOURS. 



36 

Table A. 
When hour angle is less than 6 hours, name th 3 factors taken from Table A contrary to name of lat. 





3 HOURS. 


3 


m. 


m. 


m. m. in. 


m. ! m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 







4 


8 


12 16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 




I 
















| 






85 


II*4J ii-o 10-7 


10-3 9-9 


9-6J 9-3J 8-9 8-6 8-3 


8-0 7-7 


7-4 


7-1 


6-Q 


6-6 


8 5 | 


12-7 


12-3 


n-8 11-4 


n-i 


10-7 10-3 9-9 9-6 9-2 


8-9 8-6 


8-3 


7-9 


7-6 


7'3 


86 


!4-3 


13-8 


I3'3i 12-9 


12-4 


12-0 


ii-b 


II-2 


io-8j 10-4 


10-0 9-7 


9-3 


8-9 


8-6 


8-3 


86 


16-3 


15-8 


15-2 


14-7 14-2 


13-7 


13-2 


12-8 


12-3 


11-9 


11-4 ii-o 


IO-6 IO-2 


9-8 


9-4 


87 


19-1 


18-4 


17-8 


17-2 


16-6 


16-0 15-5 


I 4 -9 


14-4 


13-9 


13-4 12-9 


12-4 n-9 


II-5 


II-O 


87* 


22-9 


22-1 


21-4 


2O-6: I9-9 


19-2 


18-5 


17-9 


17-3 


16-6 


16-0:15.4 


14-9 14-3 


I V 8 


13-2 


88 


28-6 


27-7 


26-7 


2 5 -8 


24-9 


24-0 


23-2 


22-4 


21-6 


20-8 


20-1 


19-3 


18-6 


17-9 


17-2 


16-5 


88 


38-2 


36-9 35-6 


34'4 


33-2 


32-o 


30-9 


29-8 28-8 


27-7 


26-7 


25-8 


24-8 23-9 


23-0 


22-1 


89 


57'3 


55-3 53'4 


51-6 


49-8 


48-1 


46-4 


44-8, 43-2 


41-6 


40-1 


38-6 


37-2 35- 8 


34'4 


33' 1 


89* 


H5 


in 


107 


103 


99-6 


96-2 


92-8 


89-5 86-3 


3'3 


80-2 


77-3 


74-4 7i-6 


68-9 


66-2 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




60 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 







8 HOURS. 





4 HOURS. 


3 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


in. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 







4 


8 


12 


16 


20 24 


28 


32 36 


40 


44 


48 


52 56 


60 


o 

85 
































3-o6 


6-60' 6-34 


6-08 


5-82 


5'57 


.V33 


5'9 4-85 


4-62 


4-39 


4-16 3-94 3-7i 


3-49 


3-28 


85* 


7-34' 7'4 


6-76 


6-47 


6-20 


5-93 


5-66 5-39 5-13 


4-88 


4-62 


4-38 4-13 


3-88 


3-64 


3'4 


86 
86| 


8-26 7-931 7-60 
9-44' 9 06 8-69 


7-29 
8-33 


6-97 

7-97 


6-67 
7-62 


6-37|6-o7 
7-28 6-94 


5-78 
6-61 


5-49 
6-28 


5-21 
5-95 


4-92 
5-63 


4-65 
5-3i 


4'37 
5-00 


4-10 
4-69 


3-83 
4-38 


87 


II-O 


10-6 


io-ij9-72 


9-3i 


8-90 


8-50 8-10 


7-71 7-32 


6-94 


6-57 6-20 


5-83 


5-47 


5-n 


87l 


13-2 12-7 


12-2 II'7 


II-2 


10-7 .10-2 9-72 


9-25 8-79 


8-34 


7-89 7-44 7-oo 6-57 


6-14 


88 


16-5 15-9 


15-2 14-6 


I 4 -0 


13-4 


12-7 12-2 


n-6 ii-o 


10-4 


9-86:9-30 


8-76J8-2I 


7-67 


88J 


22-1 


.M 


20-3 19-5 18-6 


17-8 


17-0 


16-2 


15-4 14-7 


13-9 


I3-I 


12-4 


11-7 ii-o 


IO-2 


89 


33-i 


.11-8 


30-5J 29-2 27-9 


26-7 25-5 


24-3 


23-2J22-0 


20-9 


19-7 


18-6 17-5 16-4 


15-4 


89i 


66-2 


63-5 


60-9 58-4 55-9 


53'4 5i-o 48-6 


46-3 44-0 


41-7 


39-5 


37'2 


35-o 


32-9 


3'7 




m. 


m. 1 


m. m. m. 


m. m. 


m. 


m. 


m. 


m. 


m. 


m. m. m. 


m. 




60 


56 ! 


52 


48 


44 


40 


36 


3*| 


28 


24 


20 


16 


12 


8 


4 







7 HOURS. 





5 HOURS. 


,1 


m. 


m. 


m. 


m. 


m. 


m. m. 


m. m. 


m. 


m. m. 


m. 


m. m. 


m. 







4 


8 


12 


16 


20 24 


1 28 


32 36 


40 44 


48 


52 56 


60 


85 






























oo 


3-06 


2-85 


2-64 2-43 


2-22 


2-02 I-8l 


1-61 


1-40 1-20 


i-oo 0-80 


0-60 


0-40 O-2O 


85! 


3'4 


3-17 2-93 


2-70 


2-47 


2-24 2-01 


1-79 


1-56 1-34 


I-II 


0-89 


0-67 


0-44 0-22 


00 


86 


3-83 


3-57J3-3 3-04 


2- 7 8 


2-52 2-27 


2-OI 


1-76 


1-50 


1-25 i-oo 0-75 


0-50 0-25 


00 


86! 


4-38 


4-08 3-77 


3-48 


3-18 


2-88 


2-59 2-30 


2-01 


1-78 


1-43 1-14 


0-86 


-57 


0-29 


00 


87 


5-n 


4-76 


4-41 


4-06 


1-71 


3-36 


3-02 


2-68 


2-34 2-01 


1-67 


i-33 


i-oo 0-67 0-33 


oo 


8 7 * 


6-14 




5-29 4-87 


4'45 


4-04 3-63 


3-22 


2-8i| 2-41 


2-00, 1-60 


1-201 0-80 


0-40 


oo 


88 


7-67 


7-14 


6-61 6-09 


5-57 


5-05 


4-54 


4'5 


3-52 3' 01 


2-51 2-OO 


1-50 i-oo 


0-50 


00 
































88! 


10 2 9-52 


8-82 8-12 


7-42 


6-73 


6-05 


5-37 


4-69 


4-01 


3-34 


2-67 


2-OO 1-33 


0-67 


oo 


89 


15-4 14-3 13-2 12-2 


ii-i 


IO-I 


9-07 


8-05 


7-03 


6-02 


5-01 


4-01 


3-OO 2-OO 


I-OO 


oo 


89! 


30-7 28-6 26-5 24-4 


22-3 


20-2 


18-1 


I6-I 


14-1 


12-0 


IO-O 


8-01 


6-01 4-00 


2-00 


oo 




m. 


m. 


m. m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




60 


56 


52 


48 


44 


40 


36 


32 


28 


24 


20 


16 


12 


8 


4 


o 




6 HOURS. 



When hour angle is more than 6 hours, name the factors taken from Table A the same as 
the name of the latitude. 



37 

Table B. 
Always name the factors taken from Table B the same as the name of declination. 



id 


3 HOURS. 




m. 


m. m. 


m. m. 


m. 


m. 


m. 


m. m. 


m. 


m. 


m. 


m. 


m. 


m. 


Q 





4 8 


12 16 


20 24 


28 i 32 36 


40 


44 


48 


52 


56 


60 


85 










i 
14-9 I4-.7 
















13-2 


I6-2JI5-9 15-6! 15-4' 15-1 


I4-5J I4-3 


14-1 


14-0 


13-8 


13-6 


13-5 


13-3 


86 L 


l8-d 17-7 17-4 17-1 16-8 

20-2 19-9 19-6! 19-2' 18-9 


18-7 18-4 


16-1 
18-1 


15-9 

17-9 


17-7 


15-5 

17-5 


I5'3] 15-2 
I7-2 1 17-1 


15-0 
16-9 


14-8 
16-7 


14-7 
16-5 


864 


23-1 


22-7 


22-4 22-0,21-7 


21-3 


21-0 


20-7, 20-5 20-2 


20-O 


I9-7| 19-5 


19-3 


19-1 


18-9 


87 


27-0 


26-5 


26-1 


25-7 


25-3 


24-9 


24-6 


24-2 


23-9 


23-6 


23-3 


23-0 22-8 


22"> 


22-3 


22-0 


874 


32-4 


31-8 


31-3 


30-8 


30-3 


29-9 


29-5(29-1 


28-7 


28-3 


28-0 


27-6 27-3 


27-0 


26-7 


26-4 


88 


4'5 ! 39-8 


39-2 


38-5 


37-9 


37'4 


36-8 


36-3 


35-9 


35-4 


35- 


34'5 


34-1 


33-8 


33-4 


33-1 


884 


04 i 5o 


52-2 


3,4 


50-6 


49-9 


49-1 


48-5 


47-8 


47-2 


46-6 


46-1 


45-5 




44-6 


44-1 


89 


81-0 79-6 


78-3 


77-1 


75-9 


74-8 


73-7 


72-7 


71-7 


70-8 


69-9 


69-1 


68-3 


67-6 


66-8 


66-2 


894 


162 159 


157 


154 


152 


15 


147 


145 


M3 


M2 


140 


138 137 


135 


134 


132 




m. m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




60 56 


52 


48 


44 


40 


36 


3 2 


28 


24 


20 


16 


12 8 


4 


o 




8 HOURS. 



s d 


4 HOURS. 


o "-J3 


m. 


m. 


m. 


m. 


m. 


m. m. 


m. 


m. 


m. 


in. 


m. 


m. 


m. 


m. 


m. 


5 





4 


8 


12 


16 


20 ! 24 


28 


32 


36 


40 


44 


48 


52 


56 


60 














/ ! x 




















85 


13-2 13-1 


12-9 


12-8 


12-7 


12-6 12-5 


12-4 


12-3 


12-2 


12-2 


I2-I 


12-0 


12-0 


n-9 


n-8 


854 


14-7 


14-5 


14-4 


I4-3 I4' 1 


14-0 13-9 


13-8 


13-7 


13-6 


13-5 I3-4 


I3-4 


13-3 


1.3-2 


13-2 


86 


16-5 


16-4 


16-2 


16-1 


15-9 






IV4 


15-3 


15-2 I5-I 


15-0 I5-0 


14-9 


14-8 


864 


18-9 


18-7 


18-5 


18-3 


18-2 


18-0 


17-9 


17-8 


17-6 


17-5 


17-4 


17-3 


17-2 


I 7 -I 


17-0 


16-9 


87 


22-C 


21-8 


21-6 


21-4 


21-2 


2I-I 


20-9 


20-7 


20-6 


20-4 


20-3 


2O-2 


20-1 


2O-O 


19-9 


19-8 


74 


26-4 


26-2 


25-9 


25-7 25-5 


25-3 


25-1 24-9 


24-7 


24-5 


24-4 


2 4 -2 


2 4 -I 


24-0 


23-8 


23-7 


88 


33-i 


32-7 


32-4 


32-1 


31-9 


3I-6J3I-3 


3i-i 


3'9 


30-7 


30-5 


30-3 


3 0-I 


29-9 


29-8 


29-6 


884 


44-1 


43'7| 43-3 


42-9 


42-5 


42-1 


41-8 


41-5 41-2 


40-9 


40-6 


40-4 


40-2 


39-9 


39-7 


39-5 


89 
894 


66-2 
132 


65-5 64-9) 64-3 
131 1130 ;i29 


63-7 

127 


63-2 
126 


62-7,62-2 61-8 
125 '124 124 


61-4 
I2 3 


61-0 

122 


60-6 
121 


60-2 
120 


59-9 

I2O 


59-6 


59-3 




m. 


m. 


m. i m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




o 


4 


8 | 12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 




7 HOURS. 



k 


5 HOURS. 


.i3 

o.2 


m. 


m. 


m. 


m. 


m. 


m. 


m. m. 


m. 


m. 


m. m. m. 


m. 


m. 


m. 


P 





4 


8 


12 16 

I 


20 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 




i 




























85 


n-8 n-8 11-7 11-7 n-6 


n-6 


n-6 


ii5 


ii") 


1 1 :5 


ii-5 


n-5 H'5 


n-4 


u-4 


n-4 


85! 


13-2 13-1! 13-0, 13-0! 13-0 


12-9 


12-9 


12-8 


12-8 


12-8 


12-8 


12-7 12-7 


12-7 


12-7 


12-7 


86 
86^ 


14-8 14-7 
16-9! 16-8 


14-7 
16-8 


14-6 14-6 
i6-7J 16-7 


14-5 
16-6 


14-5 
16-6 


14-4 
16-5 


14-4 
16-5 


14-4 
16-4 


14-4 
16-4 


14-3 
16-4 


14-3 
16-4 


14-3 
16-4 


14-3 
16-4 


14-3 
16-3 


87 


19-8 


19-7! 19-6 


19") 


19-4 


19-4 


19-3 


19-3 


19-2 


19-2 


19-2 


19-1 


19-1 


19-1 


19-1 


19-1 


V 


23-7 
29-6 


23-6 23-5 
29-5' 29-4 


23-4 
29-3 


23-3 
29-2 


23-3 
29-1 


23-2 
29-0 


23-1 23-1 23-0 

28-9 28-9: 28-8 


23-0 
28-7 


23-0 
28-7 


22-9 
28-7 


22-9 
28-7 


22-9 
28-6 


22-9 

28-6 


884 
89 


39-5 
59-3 


39'4 
59-0 


39-2 

58-8 


39-o 
58-6 


38-9 
.58-4 


38-8 
58-2 


38-7 
58-0 


38-6 
57-9 


38-5 38-4 
57'7 57-6 


38-3 
57-5 


38-3 
57'4 


38-2 

57-4 


38-2 
57-3 


38-2 
57'3 


38-2 

57'3 


894 


H9 


1x8 


118 


ii7 


H7 


116 


116 


116 


115 H5 


115 


H5 


115 


H5 


H5 


115 




m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 


m. 




o 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


44 


48 


52 


50 


60 




6 HOURS. 



3S 



Table 0. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 
Azimuth is named N or S according to the name of the A and B correction. 



A and B 


LATITUDES. 


Cor- 






























rection. 


00 


5 


10 


13 


16 


18 


20 


22 


24 


25 


26 ! 27 


28 


29 


30 














! 




i 








AZIMUTHS. 


' 








o 





o 








o 


o 


o 


o 


o 








o 


ooo 


90-0 


9o % o 


go'o 


90-0 


go'o 


gO'O 


9O'O 


9O'o 


go'o 


90-0 


90-0 


90-0 


90-0 


90-0 


90-0 


OIO 


89-4 


89-4 


89 4 


89-4 


89-4 


89-5 


89-5 


89-5 


89-5 


89-5 


89-5 


89-5 


89-5 


89-5 


89-5 


020 


88-9 


88-9 


88-9 


88-9 


88-9 


88-9 


88-9 


88-9 


89-0 


89-0 


89-0 


89-0 


8 9 -0 


89-0 


89-0 


030 


88-3 


88-3 


88-3 


88-3 


88-3 


88-4 


88-4 


88-4 


88-4 


88-4 


88-5 


88-5 


88-5 


oo. r 
oo 5 


88-s 


040 


877 


877 


8/7 


87-8 


87-8 


87-8 


87-8 


87-9 


87-9 


87-9 


87-9 


88-0 


88-0 


88-0 88-0 


050 


87-1 


87-1 


87-2 


87-2 


87-2 


87-3 


87-3 


87-3 


87-4 


87-4 


87-4 


87-4 


87-5 


87-5! 87-5 


060 


86-0 


86-6 


86-6 


867 


867 


867 


86-8 


86-8 


86-9 


86-9 


86-9 


86-9 


87-0 


87-0 87-0 


070 


86-0 


86-0 


86-1 


86-1 


86-2 


86-2 


86-2 


86-3 


86-3 


86-4 


86-4 


86-4 


86-5 


86- 5 | 86-5 


080 


85-4 


85-4 


85-5 


85-5 


85-6 


85-6 


857 


85-8 


85-8 


85-9 


85-9 


85-9 


86-0 


86-0 


86-0 


090 


84-9 


84-9 


84-9 


85-0 


85-1 


85-1 


85-2 


85-2 


85-3 


85'3 


85-4 


85-4 


85-5 


85-5 


85-5 


'TOO 


84-3 


84-3 


84-4 


84-4 


84'5 


84-5 


84-6 


847 


84-8 


84-8 


84-9 


84-9 


85-0 


85-0 


85-1 


no 


837 


837 


83-8 


83-9 


84-0 


84-0 


84-1 


84-2 


84'3 


84-3 


84-4 


84-4 


84-5 


84-5 


84-6 


- I2O 


83-2 


83-2 


33'3 


83-3 


83-4 


83-5 


83-6 


837 


837 


83-8 


83-8 


83-9 


84-0 


84-0 


84-1 


130 


82-6 


82-6 


827 


82-8 


82-9 


83*0 


83-0 


83-1 


83-2 


83'3 


83-3 


83-4 


83-5 


83-5 


83-6 


140 


82-0 


82-1 


82-1 


82-2 


82-3 


82-4 


82-5 


82-6 


827 


82-8 


82-8 


82-9 


83-0 


83-0 


83-1 


15 "" 


81-5 


8r 5 


8r6 


817 


8r8 


81-9 


82-0 


82-1 


82-2 


82-3 


82-3 


82-4 


82-5 


82-5 


82-6 


160 


80-9 


80-9 


8ro 


8ri 


81-3 


81-3 


81-4 


8i-e 


817 


817 


81-8 


81-9 


82-0 


82-0 


82-1 


170 


80-4 


80-4 


80-5 


80-6 


807 


80-8 


80-9 


81-0 


Sl'2 


81-2 


81-3 


81-4 


Si'5 


81-5 


81-6 


180 


79-8 


79-8 


79-9 


80- 1 


80-2 


80-3 


80-4 


80-5 


80 7 


807 


80-8 


80-9 


8ro 


8n 


Si-i 


IQO 


79-2 


79'3 


79'4 


79'5 


79-6 


79-8 


79-9 


80-0 


SO'2 


80-2 


80-3 


80-4 


80-5 


80-6 


807 


200 


787 


787 


78-9 


79*o 


79-1 


79*2 


79'4 


79'5 


79-6 


797 


79'S 


79-9 


80-0 


80- 1 


80-2 


2IO 


78-1 


78-2 


78-3 


78-4 


78-6 


787 


78-8 


79-0 


79'I 


79'2 


79'3 


79'4 


79'5 


79-6 


797 


220 


77-6 


77-6 


77'8 


77'9 


78-1 


78-2 


78-3 


78-5 


78-6 


787 


78-8 


78-9 


79-0 


79-1 


79-2 


230 


77-0 


77-1 


77-2 


77'4 


77'5 


777 


77-8 


78-0 


7 8-I 


78-2 


78-3 


78-4 


78-5 


78-6 


787 


2^0 


76-5 


76-6 


767 


76-8 


77-0 


77-1 


77'3 


77'5 


77-6 


777 


77-8 


77'9 


78-0 


78-1 


78-3 


250 


76*0 


76*0 


76-2 


763 


76-5 


76-6 


76-8 


76-9 


77-1 


77-2 


77'3 


77'4 


77-6 


777 


77-8 


260 


75'4 


75'5 


75-6 


75-8 


76^0 


76-1 


76-3 


76-4 


76-6 


767 


76-8 


77-0 


77-1 


77-2 


77'3 


270 


74 '9 


74'9 


75'i 


75*3 


75'5 


75-6 


75-8 


75'9 


76-1 


76-2 


76-4 


76-5 


76-6 


767 


76-8 


280 


74'4l 74'4 


74-6 


747 


74'9 


75'i 


75'3 


75'4 


757 


75-8 


75'9 


76^0 


76-1 


76-2 


76-4 


!>90 


73-8 


73'9 


74-1 


74-2 


74'4 


74-6 


74-8 


75'o 


75'2 


75'3 


75'4 


75'5 


75-6 


75-8 


75'9 


3 00 


73-3 


73'4 


73'5 


737 


73'9 


74-1 


743 


74'5 


747 


74-8 


74'9 


75'0 


75-2 


75'3 


75'4 


310 


72-8 


72-8 


73*o 


73*2 


73'4 


73 -6 


73-8 


74-0 


74-2 


74'3 


74'4 


74-6 


747 


74-8 


75'0 


3 20 


72-3 


72-3 


72-5 


727 


72-9 


73'i 


73'3 


73'5 


737 


73-8 


74-0 


74' i 


74-2 


74'4 


74' 5 


330 


717 


71-8 


72*0 


72-2 


72-4 


72-6 


72-8 


73*o 


732 


73'3 


73'5 


73'6 


73-8 


73-9 


74-1 


340 


71-2 


7i'3 


7i'5 


717 


71-9 


72-1 


72-3 


7 2 '5 


727 


72-9 


73'0 


73'i 


73'3 


73'4 


73-6 


350 


707 


70-8 


71-0 


71-2 


7i'4 


71-6 


71-8 


72-0 


72-3 


72-4 


72-5 


727 


72-8 


73 


73^ 


3 60 


70-2 


7'3 


/o-S 


707 


70-9 


71-1 


7i'3 


7!'5 


71-8 


7i-9 


72-1 


72-2 


72-4 


72-5 


727 


'37 


697 


69-8 


70-0 


JO'2, 


70-4 


70'6 


70-8 


71-1 


7i - 3 


7 I- 5 


71-6 


71-8 


71-9 


72-1 


72-2 


380 


69-2 


69-3 


69-5 


697 


69-9 


70-1 


70-3 


70-6 


70-9 


71-0 


71-1 


7i'3 


7i'5 


71-6 


71-8 


39 


687 


68-8 


69-0 


69-2 


69-4 


69-6 


69-9 


70' i 


70-4 


70-5 


707 


70-8 


71-0 


71-2 


71-3 


4 00 


68-2 


6S-3 


68-5 


687 69-0 


69-2 


69-4 


697 


69-9 


70-1 


70-2 


70-4 


705 


707 


70-9 


410 


G 77 


67-8 


68-0 


68-2 


68-5 


687 68-9 


69-2 


69-5 


69-6 


69-8 


69-9 


70-1 


70-3 


70-5 


4 20 


67-2 


67-3 


67-5 


677 


68-0 


68-2 


68-5 


687 


69-0 


69-2 


69-3 


G9-5 


697 


69-8 


70-0 


430 


667 


66-8 


67-0 


67-3 67-5 


67-8 


68-0 


68-3 


68-6 


687 


68-9 


69-0 


69-2 


69-4 


69-6 


44 


66-3 


66-3 


66-6 


66-8 


67-1 


67-3 


67-5 


67-8 


68-1 


68-3 


68-4 


68-6 


68-8 


69-0 


69-1 


450 


65-8 


65*9 


66-1 


66-3 


66-6 


66-8 


67-1 


67-4 


677 


67-8 


08-o 


68-2 


68-3 


68-5 


687 


4 60 


65-3 


65'4 


65-6 


65'9 


66-1 


66-4 


66-6 


66-9 


67^2 


67-4 


67-5 


677 


67-9 


68-1 


68-3 


470 


64-8 


64-9 


65-2 


65H 


657 


65'9 


66-2 


66-5 


66-8 


66-9 


67-1 


67-3 


67-5 


677 


67-9 


480 


64-4 


64-4 


647 


64-9 


6 5 '2 


65-5 


657 


66-0 


66-3 66-5 


667 


66-8 


67-0 67-2 


67-4 


490 


63 ! 9 


64*0 


64-2 


64-5 


64-8 


65-0 


65-3 


65-6 


65'9 


66-1 


66-2 


66-4 


66-6 


66-S; 67-0 




























i 




39 



Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 
Azimuth is named N or S according to the name of the A and P wrrection. 



A and B 
Cor- 
rection. 


LATITUDES. 


30 


00 


5 


10 


13 


16 


18 


20 


22 


24 i 25 


26 


27 


28 


29 


AZIMUTHS. 


t 


o o 








o 


o 














o 


o 


o 


o 


o 


500 


^3'4 


63'5 


63-8 


64*0 


64-3 


64-6 


64-8 


65-1 


65-5 


65-6 


65-8 


66-0 


66-2 


66-4 


66-6 


510 


63*0 


63-1 


63-3 


63-6 


63-9 


6 4 -I 


64-4 


647 


65*0 


65-2 


65*4 


65-6 


65-8 


66-0 


66-2 


520 


62-5 


62-6 


62'9 


63'! 


63-4 


637 


64-0 


64-3 


64-6 


64-8 


64-9 


65-1 


65-3 


65-5 


65-8 


530 


62-1 


62-2 


62-4 


627 


63-0 


6 3 -2 


6 3 ;s 


63-8 


64^2 


64-3 


64-5 


647 


64-9 


65-1 


65*3 


'54 


61-6 


617 


62-0 


62-2 


62-6 


62-8 




63 '4 


637 


63-9 


6 4 -I 






647 


64-9 


550 


6l'2 


61-3 


6r6 


6r8 


62-1 


62*4 


627 


63-0 


63-3 


63-5 


637 


63-9 


64-1 


64-3 


64-5 


560 


60-8 


60'8 


Sri 


6r 4 


617 


62'O 


62-2 


62-6 


62 '9 


63-1 




63*5 


637 


63-9 


64' i 


"57 


603 


60-4 


607 


6ro 




61-5 


61-8 


62-1 


62-5 


627 


62 - 9 


63-1 


63-3 


63-5 


637 


580 


59'9 


60'0 


60-3 


60-5 


60-9 


6ri 


61-4 


617 


62-1 


62-3 


62-5 


627 


62-9 


63-1 


63-3 


590 


59'5 


59-6 


59-8 


60- 1 


60-4 


607 


61*0 




617 


61*9 


62-1 


62-3 


62-5 


627 


62-9 


600 


59'0 


59'I 


59'4 


597 


60*0 


60-3 


60-6 


60-9 


6r 3 


61-5 


6i7 


61-9 


62-1 


6.3 


62-5 


610 


58-6 


587 




59'3 


59'6 


59 "9 


60-2 


60-5 




6ri 




61-5 


617 


61-9 


62-2 


620 


58-2 




58-6 


58-9 


59'2 


59'5 


59'8 


60- 1 


60-? 


607 


60-9 


6ri 


61-3 


61-5 


6r8 


630 




57'9 


58-2 


58-5 


58-8 


59' i 


59'4 


597 


60- 1 


60-3 


60-5 


607 


6o'9 


6ri 


61-4 


640 


57'4 


57*5 


57'8 


58-1 


58-4 


587 


59'o 


59-3 


S97 


59'9 


60-1 


60-3 


60-5 


60-8 


61*0 


650 


57' 


57*i 


57'4 


577 


58-0 


58-3 


58-6 


58-9 


59'3 


59'5 


597 


59'9 


60- 1 


60-4 


60-6 


660 


56-6 


567 


57' 57'3 


57'6 


57*9 


58-2 


58-5 


58*9 


59'i 


59'3 


59'5 


59-8 


60-0 


60-2 


670 


56-2 


56-3 


56-6 


56-9 


57'2 


57'5 


57'8 


58-2 


58-5 


587 


58-9 


59'2 


59'4 


59-6 


59'9 


680 


55'8 


55 ! 9 


56-2 


56-5 


56-8 




57 '4 


57-8 


58-2 


58*4 


58-6 


58-8 


59' 


59'3 


59'5 


690- 


55'4 


55'5 


55-8 


56-1 


56-4 


5?7 


57-0 


57'4 


57-8 


58-0 


58-2 


58-4 


58-6 


58-9 


59'i 


700 


55-o 


55' 1 


55'4 


557 


56-1 


56-3 


567 


57'o 


57'4 


57-6 


57-8 


58-0 


58-3 


58-5 


58-8 


710 


54'6 


547 




55'3 


557 


56-0 


56-3 


56-6 


57'Q 


57' 2 


57'5 


577 


57'9 


58-2 


58-4 


720 


54' 2 


54'3 


547 


54'9 


55'3 


55-6 


55'9 


56-3 


567 


56-9 


57'i 


57'3 


57'6 


57'8 


58-1 


73 


53'9 


54' 


54'3 


54'6 


54'9 


55'2 


55-6 


55'9 


56-3 


56-5 


567 


57' 


57' 2 


57'4 


577 


74 


53'5 






54'2 




54'9 


55'2 


55'5 


55'9 


56-2 


56-4 


56-6 


56-8 


57' i 


57'3 


75 


53'i 


53'2 


53-6 


53-8 


54*2 


54'5 


54-8 


55'2 


55-6 


55-8 


56-0 


56-2 


56-5 


567 


57' 


760 


52-8 


52*9 


53'2 


53*5 


53-8 


54' 1 


54'5 


54-8 


55'2 


55'4 


557 


55'9 


56-1 


56-4 


56-6 


77 


52-4 


52-5 


52-8 


53' 1 


53'5 


53-8 


54' 1 


54'5 


54'9 


55'i 


55'3 


55'5 


55'8 


56-0 


56-3 


780 


52-0 


52-2 


52-5 


52-8 




53'4 


53-8 


54'i 


54'5 


547 


55' 


55* 2 


55'4 


557 


56-0 


790 


51*7 


5 r8 


52-1 


52-4 


52-8 


53'i 


53'4 


53*8 


54' 2 


54'4 


54'6 


54^9 


55'i 


55'4 


55'6 


800 


51-3 


51-4 


5i-8 


52-1 


52*4 


527 


53'i 


53'4 


53-8 


54' ! 


54*3 


54*5 


54-8 


55'0 


55'3 


810 


51-0 


5 I<] 


51*4 


517 


52-1 


52-4 


527 


53'i 


53'5 


537 


53'9 


54' 2 


54'4 


547 


55' 


820 


50-6 


50-8 






51-8 


52-1 




52-8 


53*2 


53*4 


53-6 


53-8 


54* 1 


54*4 


54*6 


830 


50*3 


50-4 


507 


51-0 


5^4 


517 


52-0 


52-4 


52*8 


53' 


53*3 


53'5 


53'* 


54' 


54'3 


840 


50-0 


50-1 


50-4 


507 


5i'i 


5i'4 


517 


52-1 


52-5 


527 


52-9 


53'2 


53'4 


537 


54' 


850 


49-6 


497 


50-1 


50-4 


507 


51-0 


51-4 


51-8 


52-2 


52-4 


52-6 


52-9 


53'i 


53'4 


53'6 


860 


49'3 


49'4 


497 


50-0 


50-4 


507 


5 1 ' 1 


5 IV 


51-8 


52-1 


52-3 


52-5 


52-8 


53' 1 


53'3 


870 


49-0 


49-1 


49'4 


497 


50-1 


50-4 


507 


5 1 ' 3 


5^5 


517 


52-0 


52-2 


52-5 


527 


53* 


880 


487 


48-8 


49-1 


49'4 


49-8 


50-1 


50-4 


50-8 


51-2 


51*4 


517 


51*9 


52-2 


5 2 *' 


527 


890 


48-3 


48-4 


48-8 


49-1 


49'5 


49-8 


50-1 


50-5 


50-9 


5i'i 


50-3 


50-6 


50-8 


52-1 


52'4 


900 


48-0 


48-1 


48-4 


48-8 


49-1 


49'4 


49'8 


50-2 


50-6 


50-8 


51-0 


5^3 


5i'5 


51-8 


52-1 


910 


477 


47-8 


48-1 


48-4 


48-8 


49-1 


49'5 


49-8 


50-3 


50-5 


57 


51-0 


51-2 


5 r '5 


51-8 


920 


47'4 


47'5 


47-8 


48-1 


48*5 


48-8 


49-2 


49'5 


50-0 


50-2 


50M 


507 


50-9 


51-2 


5^5 


930 
940 


47'* 

46-8 


47'2 
46-9 


47-5 
47-2 


47-8 


48-2 
47*9 


48-2 


48-8 


49-2 
48-9 


49-6 
49'3 


49'9 
49-6 


50-1 
49-8 


50-4 
50-1 


50-6 
50*3 


50-6 


51-2 
5'9 


'950 


46-5 


46-6 


46-9 


47-2 


47-6 


47'9 


48-2 


48-6 


49-0 


49'3 


49'5 


49-8 


50-0 


50-3 


50-6 


960 
970 
980 
990 


46-2 
45'9 
45-6 

45'3 


46-3 
46-0 

457 
45*^ 


46-6 
46'; 
46-0 

457 


46-5 
4 6-C 
46-3 
4 6-c 


47'3 
47-0 
467 
46-4 


47-6 

47'3 
47-c 
467 


47'9 
477 
47'4 
47* 1 


48-0 
477 
47'5 


487 
48-5 
48-2 
47'9 


49-0 

487 
48-4 
48-1 


49'2 
48-9 
48-6 
48-3 


49'5 
49-2 
48-9 
48-6 


497 
49'4 
49-1 
48-8 


50-0 
497 
49'4 
49-1 


50'3 

497 
49'4 



Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 
Azimuth is named N or S according to the name of the A and B correction. 



AandB 


LATITUDES. 


Cor- 






























rection. 


00 5 


10 


13 


16 


18 


20 


22 


24 


25 


26 


27 


28 


29 


30 




AZIMUTHS. 


i 
I '00 


45*o 


45-1 


45'4 


457 


4 6-I 


46-4 


46-8 


47-2 


47-6 


47-8 


4 8-I 


48-3 


48-6 


48-8 


49-1 


I'02 


44'4 


44'5 


44'9 


45'2 


45*6 


45'9 


46'2 


46-6 


47-0 


47-2 


47'5 


477 


480 


48-3 


48-5 


I'O4 


43'9 


44-0 


44'3 


44-6 


45'o 


45'3 


457 


46-0 


46-5 


467 


46-9 


47-2 


47 '4 


477 


48-0 


I -06 


43'3 


43'4 


43-8 


44-1 


44'5 


44 -8 


45-i 


45'5 


45'9 


46-1 


46-4 


46-6 


46-9 


47-2 


47 - 4 


I -08 


42-8 


42-9 


43'2 


43'5 


43'9 


44' 2 


44-6 


45'0 


45'4 


45-6 


45'9 


46-1 


46-4 


4 6-6 


46-9 


no 


42-3 


42-4 


427 


43'0 


43'4 


437 


44-1 


44'4 


44'9 


45*i 


45'3 


45-6 


45'8 


46'! 


46-4 


x'ia 


4 r8 


41-9 


42-2 


42-5 


42*9 


43'2 


43'5 


43'9 


44'3 


44-6 


44-8 


45'i 


45'3 


45'6 


45'9 


1-14 


4i'3 


41-4 


417 


42'O 


42-4 


427 


43'o 


43'4 


43-8 


44-1 


44'3 


44-6 


44-8 


45'i 


45M 


ri6 


40-8 


40-9 


41-2 


4i'5 


41-9 


42-2 


42-5 


42-9 


43'3 


43-6 


43-8 


44-1 


44'3 


44-6 


44-9 


1-18 


40'3 


40-4 


407 


4 ro 


41-4 


417 


42-0 


42'4 


42-9 


43'i 


43'3 


43'6 


43-8 


44-1 


44'4 


1-20 


39-8 


39'9 


40-2 


4'5 


40-9 


41-2 


41-6 


41-9 


42-4 


42*6 


42-8 


43'i 


43'3 


43-6 


43'9 


I'22 


393 


39'4 


39-8 


40-1 


40'5 


40-8 


41-1 


4i'5 


41-9 


42-1 


42-4 


42-6 


42-9 


43'i 


43'4 


1-24 


38-9 


39-0 


39'3 


39-6 


40-0 


40*3 


40-6 


4 ro 


41-4 


417 


41-9 


42-1 


42-4 


427 


43'0 


1-26 


38-4 


38-5 


38-9 


39-2 


39'5 


39-8 


40*2 


40*6 


4 ro 


41-2 


41-4 


417 


42-0 


42-2 


42-5 


1-28 


38-0 


38-1 


38-4 


387 


39'i 


39'4 


397 


40-1 


40'5 


40-8 


4 ro 


41-2 


4i'5 


4 r8 


42-1 


r30 


37'6 


377 


38-0 


38-3 


387 


39-0 


39'3 


397 


40-1 


40'3 


40-6 


40-8 


4 ri 


4i'3 


4 r6 


I-32 


37' i 


37*3 


37'6 


37'9 


38-2 


38'5 


38-9 


39' 3 


397 


39'9 


40-1 


4'4 


40-6 


40-9 


41-2 


i '34 


367 


36-8 


37 -2 


37'4 


37-8 


38-1 


38-5 


38-8 


39'2 


39'5 


397 


39'9 


40-2 


4'5 


40-8 


1-36 


36-3 


36'4 


367 


37'0 


37 '4 


377 


38-0 


38-4 


38-8 


39'i 


39'3 


39'5 


39'8 


40-1 


40'3 


i- 3 8 


35'9 


36-0 


36-3 


36-6 


37' 


37'3 


37-6 


38 o 


38-4 


38-6 


38-9 


39'i 


39'4 


39-6 


39'9 


1-40 


35'5 


35-6 


36-0 


36-2 


36-6 


36-9 


37'2 


37'6 


38-0 


38-2 


38-5 


387 


39-0 


39'2 


39*5 


1-42 


35'2 


35'3 


35-6 


35'9 


36-2 


36-5 


36-8 


37'2 


37'6 


37'8 


38-i 


38-3 


38-6 


38-8 


39*i 


1-44 


34-8 


34-9 


35'2 


35'5 


35-8 


36-1 


36-5 


36-8 


37'2 


37'5 


377 


37'9 


38-2 


38-4 


387 


1-46 


34'4 


34'5 


34-8 


35'i 


35'5 


35-8 


36-i 


36-5 


36-9 


37' * 


37'3 


37-6 


37-8 


38-i 


38-3 


1-48 


34'0 


34'i 


34'5 


347 


35 -I 


35'4 


357 


36-1 


36-5 


367 


36-9 


37'2 


37'4 


377 


38-0 


1-50 


337 


33-8 


34'i 


34'4 


347 


35' 


35'4 


357 


36-1 


36-3 


36-6 


36-8 


37'i 


37'3 


37-6 


1-52 


33'3 


33'4 


337 


34'o 


34'4 


347 


35'0 


35'4 


35-8 


36-0 


36-2 


36-4 


367 


36-9 


37'2 


i '54 


33' 


33'i 


33'4 


337 


34'0 


34'3 


34'6 


35*o 


35'4 


35-6 


35-8 


36-1 


36-3 


36-6 


36-9 


1-56 


327 


328 


33 A 


333 


337 


34'<> 


34'3 


347 


3i'i 


35'3 


355 


35V 


360 


362 


3 6< 5 


1-58 


32-3 


32-4 


327 


33-o 


33*4 


33-6 


34' 


34'3 


347 


34'9 


35'J 


35'4 


35'6 


35'9 


36-2 


i -60 


32-0 


32-1 


32-4 


327 


33'0 


33'3 


33'6 


34'0 


34'4 


34-6 


34-8 


35'o 


35'3 


35'5 


35-8 


1-62 


317 


3i-8 


32'i 


32-4 


327 


33'o 


33'3 


337 


34' 


34*3 


34'5 


347 


35'o 


35'2 


35'5 


1-64 


3*'4 


3i-5 


31*8 


320 


32-4 


327 


33'o 


33-3 


337 


33'9 


34*2 


34'4 


34'6 


34'9 


35'i 


1-66 


31-1 


31-2 


SI'S 


317 


32-1 


32H 


327 


33'o 


33'4 


33-6 


33-8 


34'i 


343 


34-6 


34-8 


i '68 


30-8 


30-9 


3i'i 


3*'4 


31*8 


32-0 


32-4 


327 


33 - A 


33'3 


33'5 


337 


34'u 


342 


345 


170 


30-5 


30-6 


30-9 


31-1 


31-5 


317 


32-0 


32'4 


32-8 


33-o 


33'2 


33'4 


337 


33'9 


34'2 


172 


30-2 


30'3 


30-6 


30-8 


31-2 


3IH 


317 


32-1 


32-5 


327 


32-9 


33'i 


33'4 


33'6 


33'9 


!74 


29-9 


30-0 


30-3 


30'5 


30-9 


31-1 


3i'4 


31-8 


32-2 


32-4 


32-6 


32-8 


33'i 


33*3 


33-6 


176 


29-6 


297 


30-0 


30-2 


30-6 


30-9 


31-2 


3i'5 


3i-9 


32-1 


32-3 


32-5 


32-8 


33'o 


33*3 


178 


29-3 


29M 


297 


30-0 


30-3 


30-6 


30-9 


31-2 


31-6 


3i-8 


32-0 


32-2 


32-5 


327 


33'0 


i -80 


29-1 


29-1 


29-4 


297 


30-0 


30-3 


30-6 


30-9 


3i'3 


3i*5 


317 


3^9 


32-2 


32-4 


327 


1-82 


28-8 


28-9 


29-2 


29-4 


29-8 


30-0 


30*3 


37 


31-0 


31-2 


3i'4 


317 


3i'9 


32-1 


32-4 


1-84 


28-5 


28-6 


28-9 


29-2 


29-5 


297 


30-0 


3'4 


307 


30-9 


31-2 


3i'4 


31-6 


3i'9 


32'i 


1-86 


28-3 


28-4 


28-6 


28-9 


29-2 


29'5 


29-8 


30-1 


30-5 


307 


30-9 


31-1 


3i'3 


31-6 


31-8 


r88 


28-0 


28-1 


28-4 


28-6 


29-0 


29-2 


29-5 


29-8 


30-2 


30-4 


30-6 


30-8 


3i'i 


3i'3 


31-6 


1-90 


27-8 


27-8 


28-1 


28-4 


.287 


29-0 


29'3 


29-6 


29-9 


30-1 


30-4 


30-6 


30-8 


31-0 


31*3 


1-92 


27*5 


27-6 


27-5 


28-1 


28-4 


287 


29-0 


293 


297 


29-9 


30-1 


30-3 


30'5 


30-8 


31-0 


1-94 


27-3 


27-4 


27-e 


27-9 


28-2 


28-5 


287 


29-1 


29-4 


29-6 


29-8 


30-1 


30-3 


30-5 


30-8 


1-96 


27-0 


27-1 


27-1 


27-6 


28-0 


28-2 


28-5 


28-8 


29-2 


29-4 


29'6 


29-8 


30-0 


30-3 


30-5 


1-98 


26-8 


26-g 


27-2 


27-4 


277 


28'C 


28-3 


28-6 


29-0 


29-1 


29-3 


29-5 


29-8 


30-0 


30-2 



Table 0. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION 
Azimuth is named N or S according to the name of the A and B correction. 



A and B 
Cor- 
rection. 




LATITUDES. 


00 


6 


10 


13 


18 


18 


20 


22 


24 


25 


26 


27 


28 


28 


80 


AZIMUTHS. 


2*00 


26-6 


26-7 


26-9 


27-2 


27'5 


277 


28-0 


28-3 


28-7 


28-9 


29-I 


29-3 


29-5 


29'ii 


30*0 


2-05 


26-0 


26-1 


26-4 


26-6 


269 


27-2 


27-4 


277 


28-1 


28-3 


28-5 


287 


28-9 


29-1 


29-4 


2'IO 


25-5 


25-5 


25-8 


26-O 


26-4 


26-6 


26-9 


27-2 


27'5 


277 


27-9 


28-1 


28-3 


28-6 


28-8 


2-15 


24-9 


25-0 


25'3 


25-5 




26-1 


26-3 


26-6 


27-0 


27-2 


27-4 


2 7 -6 


2 7 -8 


28-0 


28'2 


2'2O 


24-4 


24-5 


2 4 -8 


25-0 


25*3 


25*5 


25-8 


26-1 


26-5 


26-6 


26-8 


2 7 -0 


27-2 


27-5 


277 


2'25 


24-0 


24-0 




24'5 


24-8 


25-0 


25-3 


25-6 


25^ 


26-1 


26-3 


26-5 


26-7 


26-9 


27-2 


2-30 


23-5 


23-6 


23-8 


2 4 -0 


24*3 


24-6 


24-8 


25-1 


25-5 


2 5 '6 


25*8 


26-O 


26'2 


26-4 


26-7 


2-40 


22-6 


22-7 


22-9 


23-2 


23*4 


237 


23'9 


24-2 


24-5 


24-7 


24-9 


25*1 


25'3 


25-5 


25*7 


2-50 


21-8 


21-9 


22'I 


22-3 


22-6 


22-8 


23-1 


23*3 


23-6 


23*8 


24-0 


24-2 


24-4 


24-6 


24-8 


2'60 


21'0 




2I-3 


21'5 


21'8 


22"O 


22 '3 


22-5 


22-8 


23-0 


23-2 


23'3 




237 


23-9 


2-70 


20-3 


20-4 


20-6 


20-8 


2I-I 


21'3 


21'5 


21'8 


22'I 


22'2 


22-4 


22-6 


22'8 


23-0 


23-2 


2'80 


19-7 


197 


I9-9 


20- 1 


20-4 


20-6 


20-8 


2I'I 


21'4 


21'5 


217 


21-8 


22-0 


22*2 


22-4 


2-90 


I9-0 


19-1 


19*" 


I 9'5 


I9-7 


I9-9 


2O'2 


20'4 


20'7 


20*8 


21-0 


21'2 


21*3 


21-5 


217 


3'00 






I8 7 


18-9 


I9-I 


I9-3 


19-5 




2O'O 


2O'2 


2O'3 


20-5 


20-7 


2O'9 




3-10 


I7-9 


17-9 


18-1 


18-3 


18-6 


187 


l8- 9 


19-2 


I9-4 


I9-6 


I9-7 


I9-9 


20-1 


20*2 


20-4 


3 -20 


I7 - 4 


I7 - 4 


17-6 


i 7 ;8 


18-0 


18-2 


18-4 


18-6 


18-9 


I9-0 


I9-2 


i9'3 


19*5 


I9-7 


19-8 




I6'9 


I6'9 


17-1 




*7'5 


177 


17-9 


18-1 


18-4 


18*5 


18-6 


18-8 


18-9 


I9-I 


19-3 


3 '40 


l6- 4 


l6- 4 


16-6 


i6i 


17-0 


17-2 




17-6 


17-8 


18-0 


18-1 


18-3 


18-4 


18-6 


18-8 


3-60 


15*' 


15-6 


15-8 


I5-9 


16-1 


16-3 


i6'< 


167 


16-9 


17-0 


17-2 


17*3 




17-6 


17*8 




147 


! 4 '8 


15-0 




I5-3 


15-5 


15-6 


15-8 


16-1 


16-2 


16-3 


16-5 


16-6 


16-7 


16-9 


4-00 


I4-0 


I4-I 


14-2 


14-4 


14-6 


14-7 


14-9 


I5*i 


I5-3 


I5'4 


I5-5 


I57 


15*8 


16-0 


16-1 


4-20 


13*4 




13-6 


137 




14-1 


14-2 


14-4 


14-6 


14-7 


14-8 


15*0 




15*2 


15*4 


4-40 


12-8 


12-9 


13*0 


13-1 


I3-3 


13-4 


13-6 


13-8 


14-0 


14-1 


14-2 




14-4 


14-6 


147 


4-60 


12-3 


12" 


I2V 


12-6 


127 


12-9 


13-0 


13-2 


I3-4 




13-6 


137 


13-8 


14-0 


14-1 


4-80 


11-8 


n-8 


n-g 


I2-I 


I2'2 


12-4 


12-5 


127 


I2'8 


I2'9 


13-1 








13*5 


5;oo 


n'3 


11-4 


"'5 


n-6 


n-8 


11-9 


I2'O 


I2'2 


12-3 


12-4 


12-5 


127 


12-8 


12-9 


13-0 




10-3 


1C'; 


10-5 


10-6 


107 


10-8 


II'O 


II'I 


11-3 




ii -4 


ii"5 


n-6 


117 


11-9 


6'oo 


9"* 


9'5 


9-6 


97 


9-8 


9-9 


IO* I 


IO-2 


IO'? 


10-4 


IO' C 


10-6 


107 


10-8 


10-9 


6-50 


87 


8-8 


8-g 


9-0 


9-1 


9-2 


9'3 


9'4 


9'6 


9-6 


97 


9-8 


9-9 


IO'O 


IO'I 


7'oo 


8-1 


8-2 


8-3 


8-3 




8'5 


8-6 


8-8 


8-9 


9-0 


9-0 


9-1 


9-2 


9*3 


9*4 


8-0 


7-1 


7-2 


7-2 


7'3 


7'4 


7*5 


7-6 


77 


7-8 


7-9 


7'9 


8-0 


8-1 


8'i 


8-2 


9-0 


6-3 


6-4 


6-4 




6-6 


6-7 


67 


6-8 


6-9 


7*O 


7-0 


7' 1 


7-2 


7-2 


7'3 


lO'O 


57 


57 


5'* 


5-0 


5'9 


6-0 


6-1 


6-2 


6-2 


6-3 


6-3 


6-4 






6-6 


II'O 






5" 


5'3 


5'4 


5'5 


5'5 


5*6 


57 


57 


5'^ 


5-8 


5*9 


5'9 


6-0 


I2'0 


4-8 


4-8 


4-8 


4*9 








5'i 




5'3 


5*3 


5*3 


5'4 


5*5 


5*5 


13-0 


4*4 


4'4 


4'5 


4*5 


4-6 


4-6 


47 


47 


4-8 


4'9 


4*9 


4'9 


5*o 


5*o 


5'i 


15-0 


3'^ 


3'^ 


3'9 


3'9 


4-0 


4-0 


4*1 


4*i 


4-2 


4-2 


4 '2 


4'3 


4*3 


4'4 


4'4 


17-0 


3'4 


3*4 


3'4 


3'5 


3'5 


3'5 


3-6 


3-6 


37 


37 


37 


3*8 


3'8 


3*8 


3*9 


2O'O 


2-9 


2-9 


2-g 


2-9 




3-0 


3-0 




3 - i 


3*2 


3'2 


3*2 


3'2 


3*3 


3'3 


25-0 


2-3 


2*3 


2-3 


2-4 


2-4 


2-4 


2-4 


2-5 


2'5 


2*5 


2*5 


2-6 


2'6 


2-6 


2-6 


30-0 


1-9 


i -9 


rg 


2'O 


2-0 


2-0 


2'O 


2'I 


2-1 


2-1 


2-1 


2'I 


2'2 


2'2 


2'2 


40-0 


**4 




i** 


I-5J I'5 


I -5 


i'5 


"t'5 


1-6 


1-6 


1-6 


1-6 


r6 


1-6 


17 


50-0 


i'i 


I"2 


1-2 


I'2 I'2 


I '2 




I"2 


i*3 


1*3 


1-3 


i"3 


i*3 


1*3 


1*3 


70-0 


0-8 


0-8 


0-8 


o'8 0-9 


0-9 


o'9 


0-9 


0-9 


0-9 


0-9 


0-9 


0-9 


0-9 


0-9 


lOO'O 


0-6 


0-6 


0-6 


0-6 


0-6 


0-6 


0-6 


0-6 


0-6 


0-6 


0-6 


0-6 


0-6 


0-7 


0-7 


150-0 


0-4 


0-4 


0-4 


0-4 


0-4 


0-4 


0-4 


0-4 


0-4 


0-4 


0-4 


o*4 


o*4 


o*4 


0-4 


2OO'O 


'2 


O" 


O"' 


0-3 


0-3 


o'3 


0-3 


0-3 


0-3 


0-3 


0-3 


0*3 


'3 


03 


03 


300-0 


O'2 


0-2 


O'2 


O'2 


O'2 


O'2 


0-2 


0-2 


O-2 


O-2 


0-2 


O'2 


0-2 


O-2 


0-2 


400-0 


o-i 


O'l 


O'l 


O'l 


o-i 


O-2 


O'2 


0-2 


O-2 


O-2 


0-2 


O-2 


0-2 


0-2 


O'2 


800-0 


o-i 


o-i 


O'l 


O'l 


o-i 


O'l 


o-i 


o-i 


o-i 


o-i 


O'l 


o-i 


O'l 


o-i 


O'l 



Table C. 
AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 

Azimuth is named N or S according to the name of the A and B correction. 



AandB 
Cor- 
rection. 


LATITUDES. 


31 


32 


33 


34 


35 


36 37 


38 


39 


40 


41 


48 


43 


44 


45 




AZIMUTHS. 






000 


9O'o 


go'o 


90*0 


90*0 


90-0 


gO'O 


90-0 


90-0 


90-0 


go'o 


90-0 


90-0 


90-0 


90-0 


9O'0 


oio 


89-5 


89-5 


89-5 


89-5 


89'5 


89-5 


89-5 


89-5 


89-6 


89-6 


89-6 


89-6 


89-6 


89-6 


89-6 


020 


89-0 


89-0 


89-0 


89-1 


89-1 


8 9 -I 


89-1 


8 9 -l 


8 9 -I 


89-1 


89-1 


89-1 


8 9 -2 


89-2 


89-2 


030 


88-5 


88-5 


88-6 


88-6 


88-6 


88-6 


88-6 


88-6 


887 


887 


887 


887 


887 


88-8 


88-8 


040 


88-0 


88-1 


88-1 


88-1 


88-1 


88-1 


88-2 


88-2 


88-2 


88-2 


88-3 


88-3 


88-3 


88-4 


88-4 


050 


87-5 


87-6 


87-6 


87-6 


877 


877 


877 


877 


8 7 '8 


87-8 


87-8 


87-9 


87-9 


87-9 


88-0 


060 


87-1 


87-1 


87-1 


87-2 


87-2 


87-2 


873 


87-3 


87-3 


87H 


87-4 


87H 


87-5 


87-5 


87-6 


070 


86-6 


86-6 


86-6 


867 


867 


86-8 


86-8 


86-8 


86-9 


86-9 


87-0 


87-0 


8 7 -I 


87-1 


87-2 


080 


86-1 


86-1 


86-2 


86-2 


86-3 


86-3 


86-3 


86-4 


86-4 


86-5 


86-5 


86-6 


867 


867 


86-8 


090 


85-6 


85-6 


857 


857 


85-8 


85-8 


85'9 


85-9 


86-0 


86-1 


86-1 


86-2 


86-2 


86-3 


86-4 


100 


85-i 


85-2 


85-2 


85-3 


85-3 


85-4 


85-4 


85-5 


85-6 


85-6 


857 


857 


85-8 


85-9 


86-0 


no 


84-6 


847 


847 


84-8 


84-9 


84-9 


85-0 


85-0 


8 5 'i 


85-2 


85-3 


85-3 


85-4 


85'5 


85-6 


I2O 


84-1 


84-2 


84-3 


84-3 


84-4 


8 4 -5 


84-5 


84-6 


847 


847 


84-8 


84-9 


85-0 


85-1 


85-1 


130 


83-6 


837 


83-8 


83-8 


83-9 


84-0 


84-1 


84-2 


84-2 


84-3 


84H 


84-5 


84-6 


847 


847 


I 4 


83-2 


83-2 


83-3 


83-4 


83-5 


83-5 


83-6 


837 


83-8 


83'9 


84-0 


84-1 


84-2 


84-2 


84'3 


150 


827 


82-8 


82-8 


82-9 


83-0 


83-1 


83-2 


83-3 


83-4 


83'4 


83-5 


83-6 


837 


83-8 


83-9 


160 


82-2 


82-3 


82-4 


82-4 


82-5 


82-6 


827 


82-8 


82-9 


83-0 


83-1 


83-2 


83'3 


83-4 


83-5 


170 


817 


8r8 


81-9 


82-0 


82-1 


82-2 


82-3 


82-4 


82-5 


82-6 


827 


82-8 


82-9 


83-0 


83-1 


180 


81-2 


81-3 


81-4 


8i'5 


81-6 


817 


8r8 


81-9 


82-0 


82-1 


82-3 


82-4 


82-5 


82-6 


827 


190 


807 


80-8 


80-9 


8ro 


81-2 


81-3 


81-4 


81-5 


8r6 


817 


81-8 


82-0 


82-1 


82-2 


82-3 


200 


80-3 


80-4 


80-5 


80-6 


807 


80-8 


80-9 


8ro 


81-2 


81-3 


81-4 


8i-5 


817 


8r8 


82-0 


'2IO 


79-8 


79'9 


80-0 


80- 1 


80-2 


80-4 


80-5 


80-6 


807 


80-9 


8ro 


8ri 


81-3 


81-4 


8r6 


'220 


79'3 


79'4 


79*5 


797 


79-8 


79-9 


80-0 


80-2 


80-3 


80-4 


80-6 


807 


80-9 


8ro 


81-2 


230 


78-8 


79-0 


79-1 


79-2 


79'3 


79'5 


79-6 


797 


79'9 


80-0 


80-2 


80-3 


80-5 


80-6 


80-8 


140 


78-4 


78-5 


78-6 


787 


78-9 


79-0 


79-1 


79'3 


79*4 


79-6 


797 


79'9 


80-0 


80-2 


80-4 


250 


77*9 


78-0 


78-2 


78-3 


78-4 


78-6 


787 


78-9 


79-0 


79-2 


79'3 


79'5 


79-6 


79-8 


80-0 


260 


77'4 


77-6 


777 


77-8 


78-0 


78-1 


78-3 


78-4 


786 


787 


78-9 


79-1 


79'2 


79'4 


79-6 


270 


77-0 


77-1 


77-2 


77'4 


77'5 


777 


77-8 


78-0 


78-1 


78-3 


78-5 


787 


78-8 


79-0 


79-2 


280 


76-5 


76-6 


76-8 


76-9 


77-1 


77-2 


77'4 


77'6 


777 


77'9 


78-1 


78-2 


78-4 


78-6 


78-8 


290 


76^0 


76-2 


76-3 


76-5 


76-6 


76-8 


77-0 


77-1 


77'3 


77'5 


777 


77-8 


78-0 


78-2 


78-4 


300 


75-6 


757 


75'9 


76-0 


76-2 


76-4 


76-5 


767 


76-9 


77-1 


77-2 


77'4 


77-6 


77-8 


78-0 


310 


75'i 


75*3 


75'4 


75-6 


75-8 


75'9 76-1 


76-3 


76-5 


76-6 


76-8 


77-0 


77-2 


77'4 


77-6 


3 20 


747 


74'8 


75 - o 


75'i 


75'3 


75*5 


757 


75*8 


76-0 


76-2 


76-4 


76-6 


76-8 


77-0 


78-3 


330 


74-2 


74'4 


74'5 


747 


74*9 


75-1 


75'2 


75'4 


75-6 


75-8 


76-0 


76-2 


76-4 


76-6 


76-9 


34<> 


73-8 


73'9 


74'i 


74'3 


74'4 


74-6 


74-8 


75'0 


75'2 


75'4 


75-6 


75-8 


76-0 


76'3 


76-5 


350 


73'3 


73'5 


73'6 


73-8 


74-0 


74-2 


74'4 


74-6 


74-8 


75-o 


75-2 


75'4 


75-6 


75'9 


76-1 


3 60 


72-9 


73'0 


73'2 


73-4 


73-6 


73-8 


74-0 


74-2 


74*4 


74-6 


74-8 


75'o 


75'2 


75'5 


757 


370 


72-4 


72-6 


72-8 


72-9 


73'i 


73*3 


73'5 


737 


74-0 


74-2 


74'4 


74-6 


74'9 


75'i 


75'3 


3 80 


72-0 


72-1 


72-3 


72'5 


727 


72-9 


73'i 


73'3 


73'5 


73-8 


74-0 


74-2 


74'5 


747 


75'o 


390 


7 I- 5 


717 


71-9 


72-1 


72-3 


72-5 


727 


72-9 


73'i 


73'4 


73'6 


73'8 


74-1 


74'3 


74-6 


4 00 


71-1 


7i-3 


7 1 '5 


717 


71-9 


72-1 


72'3 


72'5 


727 


73-0 


73'2 


73'4 


737 


73'9 


74-2 


4 JO 


70-6 


70-8 


71-0 


71-2 


7i*4 


71-6 


71-9 


72-1 


72-3 


72-6 


72-8 


73'i 


73 '3 


73-6 


73'8 


4 20 


70-2 


70-4 


70-6 


70-8 


71-0 


71-2 


7i'5 


717 


71-9 


72-2 


72-4 


727 


72-9 


73'2 


73'5 


430 


69-8 


70-0 


70-2 


70-4 


70-6 


70-8 


71-0 


7 r> 3 


7i-5 


71-8 


72-0 


72-3 


72-5 


72-8 


73'i 


44 


69-3 


69-5 


697 


70-0 


70-2 


70-4 


7O'6 


70-9 


71-1 


7i '4 


71-6 


71-9 


72-2 


72-4 


727 


'450 


68-9 


69-1 


69-3 


69-5 


698 


70-0 


70-2 


7<>'5 


707 


71-0 


71-2 


7*' 5 


71-8 


72-1 


72-3 


460 


68-5 


687 


68-9 


69-1 


69-4 


69-6 


69-8 


70-1 


70-3 


70-6 


70-9 


71-1 


7*'4 


717 


72-0 


470 


68-1 


68-3 


68-5 


687 


68-9 


69-2 


69-4 


697 


69-9 


70-2 


70-5 


707 


71-0 


7*'3 


71-6 


480 


67-6 


67-9 


68-1 


68-3 


68-5 


68-8 


69-0 


69-3 


69-5 


69-8 


70-1 


70-4 


707 


71-0 


7*'3 


490 


67-2 


67-4 


677 


67-9 


68-1 


68-4 


68-6 


68-9 


69-2 


69-4 


697 


70-0 


7'3 


7O'C 


70-9 



Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 
Azimuth is named N or S according to the name of the A and B correction. 



AandB 
Cor- 
rection. 


n 


LATITUDES. 


32 j 33 


34 35 


36 


37 , 38 


39 40 


41 42 


43 


44 


45 


AZIMUTHS. 


i 


o 


o 


o 





o 


o 


o 


o 


o 


o 


o 


o 


o 


o 





500 


66-8 


67-0 


67-2 


67-5 


677 


68-0 


68-2 


68-5 


68-8 


69-0 


69-3 


69-6 


69-9 


70-2 


7<>'5 


510 


66-4 


66-6 


66-8 


6 7 -I 


67-3 


67-6 


67-8 


68-1 


68-4 


687 


68-9 


69-2 


69-5 


69-9 


70-2 


520 


66-0 


66-2 


66-4 


667 


66-9 


67-2 


67-4 


677 


68'0 


68-3 


68-6 


68-9 


6 9 -2 


69-5 


69-8 


'53 


65-6 


65-8 


66-0 


66-3 


66-5 


66-8 


67-1 


67'3 


67-6 


67-9 


68-2 


68-5 


68-8 


6 9 -I 


69-5 


540 


65-2 


65'4 


65-6 


65-9 


66-1 


66-4 


667 


66-9 


67-2 


67-5 


67-8 


68-1 


68-4 


68-8 


69-1 


550 


64-8 


65-0 


65-2 


65-5 


657 


66-0 


66-3 


66-6 


66-9 


67*2 


67-5 


67-8 


68-1 


68-4 


687 


560 


64-4 


64-6 


64-8 


65-1 


65-4 


65-6 


65-9 


66-2 


66-5 


66-8 


67-1 


67-4 


677 


68-1 


684 


"57 


64-0 


64-2 


64-5 


647 


65-0 


65-2 


65-5 


65-8 


66-1 


66-4 


667 


67*0 


67-4 


677 


68-0 


580 


63-6 


63-8 


64-1 


64-3 


64-6 


64-9 


65-1 


65-4 


657 


66-0 


66-4 


667 


67-0 


67-4 


677 


590 


63-2 


63-4 


637 


63-9 


64*2 


64-5 


64-8 


65-1 


65'4 


657 


66-0 


66-3 


667 


67-0 


67-4 


600 


62-8 


63-0 


63-3 


63-6 


63-8 


64-1 


64-4 


647 


65 'o 


65-3 


65-6 


66-0 


66-3 


667 


67 o 


610 


62-4 


62-6 


62-9 


63-2 


63-4 


637 


64-0 


64-3 


64-6 


65-0 


65-3 


65-6 


66-0 


66-3 


667 


620 


62*0 


62-3 


62-5 


62-8 


63-1 


63-4 


637 


64-0 


64-3 


64-6 


64-9 


65-3 


65-6 


66-0 


66-3 


630 


61-6 


61-9 


62-1 


62-4 


627 


63-0 


03-3 


63-6 


63-9 


64-2 


64-6 


64-9 


65-3 


65-6 


66-0 


640 


61-3 


61-5 


61-8 


62-1 


62-3 


62-6 


62-9 


63-2 


63-6 


63-9 


64-2 


64-6 


64-9 


653 


657 


650 


60-9 


61-1 


61*4 


617 


62*0 


62-3 


62-6 


62-9 


63-2 


63-5 


63-9 


64-2 


64-6 


64-9 


65-3 


660 


60-5 


60-8 


6ro 


61-3 


6r6 


61-9 


62-2 


62-5 


62-8 


63-2 


63-5 


63-9 


64-2 


64-6 


65*0 


670 


60-1 


60-4 


607 


60-9 


61-2 


6r 5 


61-8 


'62-2 


62-5 


62-8 


63-2 


63-5 


63-9 


64-3! 647 


680 


59'8 


6o - o 


60-3 


60-6 


60-9 


61-2 


61-5 


61-8 


62-1 


62-5 


62-8 


63-2 


63-6 


63-9 


64-3 


690 


59'4 


597 


59-9 


6O'2 


60-5 


60-8 


6ri 


61-5 


61-8 


62-1 


62-5 


62*9 


63-2 


63-6 


64-0 


700 


59'0 


59*3 


59-6 


59'9 


60-2 


60-5 


60-8 


6ri 


6r 5 


6r8 


62-2 


62-5 


62'9 


63-3 


637 


710 


587 


58-9 


59'2 


59'5 


59'8 


60- 1 


60-4 


60-8 


6ri 


61-5 


6r8 


62-2 


62-6 


62-9 


63-3 


720 


58-3 


58-6 


58-9 


59'2 


59'5 


59'8 


60- 1 


60-4 


60-8 


61-1 


61-5 


61-9 


62-2 


62-6 


63-0 


73 


58-0 


58-2 


58'5 


58-8 


59'i 


59'4 


59-8 


60- 1 


60-4 


60-8 


6ri 


61-5 


61-9 


62-3 


627 


740 


57'6 


57 '9 


58-2 


58-5 


58-8 


59'i 


59 - 4 


59-8 


60- 1 


60-5 


60-8 


6l'2 


6r6 


62-0 


62-4 


750 


57'3 


57'5 


57-8 


58-1 


58-4 


58-8 


59'i 


59'4 


59'8 


60- 1 


60-5 


60-9 


61-3 


617 


62-1 


760 


56-9 


57' 2 


57*5 


57-8 


58-1 


58-4 


587 


59'i 


59'4 


59-8 


60-2 


60-5 


60-9 


61-3 


617 


770 


56-6 


56'9 


57'i 


57'4 


57-8 


58-i 


58-4 


58-8 


59'i 


59'5 


59*8 


60-2 


60-6 


6ro 


61-4 


780 


56-2 


56-5 


56-8 


57' 1 


57 '4 


577 


58-1 


58-4 


58-8 


59'i 


59'5 


59-9 


60-3 


607 


6ri 


790 


55'9 


56-2 


56-5 


56-8 


57'i 


57'4 


57-8 


5 8-i 


58-5 


58-8 


59'2 


59-6 


60-0 


60-4 


60-8 


800 


55-6 


55-8 


56-1 


56-4 


56-8 


57'i 


57*4 


57-8 


58-1 


58-5 


58-9 


59'3 


597 


60- 1 


60-5 


810 


55*2 


55'5 


55-8 


56-1 


56-4 


56-8 


57'i 


57*4 


57'8 


58-2 


58-6 


59-0 


59'4 


59-8 


60-2 


820 


54'9 


55'2 


55'5 


55-8 


56-1 


56-4 


56-8 


57' 1 


57'5 


57*9 


58-2 


58-6 


59-o 


59'5 


59*9 


830 


54'6 


54'9 


55'2 


55*5 


55-8 


56-1 


56-5 


56-8 


57'2 


57-6 


57'9 


58-3 


587 


59-2 


59'6 


840 


54'2 


54'5 


54-8 


55'i 


55'5 


55-8 


56-1 


56-5 


56-9 


57'2 


57-6 


58-0 


58-4 


58-9 


59'3 


850 


53*9 


54'2 


54'5 


54-8 


55'2 


55'5 


55'8 


56-2 


56-6 


56'9 


57'3 


577 


58-1 


58-6 


59'0 


860 


53'6 


53*9 


54*2 


54'5 


54'8 


55'2 


55'5 


55'9 


56-2 


56-6 


57'0 


57'4 


57*8 


58'3 


587 


870 


53'3 


53-6 


53'9 


54 '2 


54'5 


54'9 


55'2 


55-6 


55'9 


56-3 


567 


57'i 


57*5 


58-0 


58-4 


880 


53'Q 


53'3 


53'6 


53'9 


54*2 


54'6 


54'9 


55'3 


55-6 


56-0 


56-4 


56-8 


57'2 


577 


58-1 


890 


527 


53'0 


53'3 


53-6 


53'9 


54'2 


54'6 


55'0 


35'3 


557 


56-1 


56-5 


56'9 


57'4 


57'8 


900 


52'4 


52'6 


53*0 


53'3 


53-6 


53'9 


54*3 


547 


55'0 


55'4 


55-8 


56-2 


56-6 


5 n 


57'5 


910 


52-0 


52-3 


52-6 


53'0 


53'3 


53'6 


54-o 


54'4 


547 


55'i 


55'5 


55'9 


56-4 


56-8 


57*2 


920 


517 


52-0 


52'3 


527 


53'0 


53'3 


537 


54'i 


54*4 


54'8 


55'2 


55*6 


56-1 


56-5 


57'0 


930 


5i'4 


517 


52-0 


52-4 


527 


53*0 


53'4 


53-8 


54*i 


54-5 


54*9 


55'4 


55*8 


56-2 


567 


940 


5i'i 


5i*4 


517 


52-1 


52-4 


527 


53'i 


53'5 


53'9 


54*2 


54'6 


55'i 


55'5 


55'9 


56'4 


950 


50-8 


5i'i 


5i'5 


5i'8 


52-1 


52-5 


52-8 


53'2 


53-6 


54* 


54'4 


54-8 


55'2 


557 


56-1 


960 


50-5 


50-9 


51-2 


5i-5 


51-8 


52-2 


52-5 


52-9 


53'3 


537 


54' 1 


54*5 


54'9 


55'4 


55'8 


970 


50'3 


50-6 


50-9 


51-2 


5i'5 


5i-9 


52-2 


52-6 


53-0- 


53'4 


53'8 


54*2 


54'6 


55-J 


55'6 


980 


50-0 


50'3 


50-6 


50-9 


51-2 


51-6 


52-0 


52-3 


527 


53-i 


53-5 


53'9 


54'4 


54'8 


55'3 


990 


497 


50-0 


53'3 


50-6 


51-0 


5i'? 


517 


52-0 


52H 


52'8 


53'2 537 


54'i 


54'5 


55'0 



Table C, 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 
Azimuth is named N or S according to the name of the A and B correction. 



A and B 
Cor- 
rection. 


LATITUDES. 


31 33 

i 


33 


34 


35 


36 


37 


38 


39 


40 


41 


42 


43 


44 


45 








AZIMUTHS. 


I'OO 


49'4 


497 


50-0 


50-3 


507 


5i'0 


5IM 


SI'S 


52-1 


52^ 


53'0 


53'4 


53'8 


54'3 


547 


ro2 


48-8 


49-1 


49'5 


49-8 


50-1 


50-5 


50-8 


51'2 


51-6 


52-0 


52-4 


52-8 


53'3 


537 


54*2 


1-04 


48" 


48-6 


48-9 


49-2 


49-6 


49'9 


50-3 


507 


51-1 


5i'5 


5i-9 


52-3 


527 


53-2 


537 


i -06 


47- 


48-0 


48-4 


487 


49-0 


49'4 


49-8 


50-1 


50-5 


50-9 


SI'S 


51-8 


52-2 


527 


53'i 


i -08 


47' 


47'5 


47-8 


48-2 


48-5 


48-9 


49-2 


49-6 


50-0 


50H 


50-8 


51*2 


517 


52-2 


52-6 


no 


46- 


47-0 


47'3 


476 


48-0 


48-3 


487 


49-1 


49-5 


49'9 


50-3 


507 


51-2 


51-6 


52-1 


ri2 


46- 


46-5 


46-8 


47-i 


47'5 


47-8 


48-2 


48-6 


49-0 


49'4 


49-8 


50-2 


507 


5i'i 


5i-6 


1-14 


45' 


46*0 


46-3 


46-6 


47-0 


47*3 


477 


48-1 


48-5 


48-9 


49'3 


497 


50-2 


50-6 


5i'i 


ri6 


45' 


45'5 


45-8 


46*1 


46-5 


46-8 


47-2 


47-6 


48-0 


48-4 


48-8 


49'2 


497 


50-2 


50-6 


ri8 


447 


45'0 


45'3 


45-6 


46-0 


46-3 


467 


47-1 


47'5 


47'9 


48-3 


48-8 


49'2 


497 


50-2 


I '20 


44-2 


44'5 


44-8 


45'i 


45'5 


45'8 


46-2 


46-6 


47-0 


47*4 


47-8 


48-3 


487 


49'2 


497 


I '22 


437 


44-0 


44'3 


447 


45-o 


45'4 


457 


46-1 


46-5 


46-9 


47'4 


47-8 


48-3 


487 


49-2 


I-2 4 


43'3 


43'6 


43'9 


44*2 


44-6 


44'9 


45'3 


457 


46-1 


46-5 


46-9 


47'3 


47'8 


48-3 


48-8 


1-26 


42-8 


43'i 


43'4 


43-8 


44-1 


44'5 


44'8 


45'2 


45-6 


46-0 


46-4 


46-9 


47*3 


47-8 


48-3 


1-28 


42-3 


427 


430 


43'3 


43'6 


44-0 


44 '4 


44'8 


45'2 


45-6 


46*0 


46-4 


46-9 


47*4 


47'9 


I-30 


41-9 


42-2 


42-5 


42-9 


43'2 


43'6 


43'9 


44'3 


447 


45'i 


45'5 


46-0 


46-4 


46-9 


47'4 


1-32 


4i '5 


41-8 


42-1 


42-4 


42-8 


43'i 


43'5 


43-9 


44'3 


447 


45'i 


45-6 


46-0 


46-5 


47-0 


i '34 


41-0 


41-3 


417 


42-0 


42-3 


427 


43'i 


43'4 


43'8 


44'3 


447 


45'i 


45-6 


46-1 


46-5 


i'36 


40-6 


40-9 


41-2 


41-6 


41-9 


42-3 


42-6 


43'o 


43'4 


43-8 


44'3 


447 


45'2 


45'6 


46-1 


1-38 


40-2 


40'5 


40-8 


41-2 


4i'5 


41-9 


42-2 


42-6 


43 - o 


43'4 


43-8 


44'3 


447 


45'2 


457 


1-40 


39'8 


40-1 


40-4 


407 


41-1 


41-4 


41-8 


42-2 


42-6 


43'<> 


43'4 


43'9 


44'3 


44-8 


45'3 


1-42 


39'4 


397 


40-0 


40-3 


407 


41-0 


41-4 


41-8 


42-2 


42-6 


43'0 


43'5 


43'9 


44 '4 


44'9 


1-44 


39-0 


39'3 


39'6 


39'9 


4<>'3 


40-6 


41-0 


41-4 


41-8 


42-2 


42-6 


43'i 


43'5 


44-0 


44'5 


r 4 6 


38-6 


38-9 


39'2 


39-6 


39'9 


40*3 


40-6 


41-0 


41-4 


41-8 


42-2 


427 


43'i 


43-6 


44-1 


r 4 8 


38-2 


38-5 


38-9 


39-2 


39'5 


39'9 


40-2 


40*6 


41-0 


41-4 


41-8 


42-3 


427 


43'2 


437 


1-50 


37'9 


38-2 


38-5 


38-8 


39'i 


39'5 


39'9 


40-2 


40-6 


41-0 


4i'5 


41-9 


42-4 


42-8 


43*3 


1-52 


37'5 


37-8 


38-1 


38-4 


38-8 


39'i 


39'5 


39'9 


40-2 


407 


41-1 


4i'5 


42-0 


42-4 


42-9 


i '54 


37'i 


37'4 


377 


38-1 


38-4 


38-8 


39'i 


39'5 


39'9 


40-3 


407 


41-1 


41-6 


42-1 


42-6 


1-56 


36-8 


37'i 


37'4 


377 


38-0 


38-4 


38-8 


39-i 


39'5 


39'9 


40'3 


40-8 


41-2 


4i7 


42-2 


1-58 


36-4 


367 


37'0 


37'4 


377 


38-0 


38-4 


38-8 


39-2 


39'6 


40-0 


40-4 


40-9 


4i'3 


4 r8 


I -60 


36-1 


36-4 


367 


37'0 


37*3 


377 


38-0 


38-4 


38-8 


39-2 


39-6 


40-1 


40'5 


41-0 


4i'5 


1-62 


35-8 


36-1 


36-4 


367 


37-o 


37'3 


377 


38-1 


38-5 


38-9 


39'3 


397 


40-2 


40-6 


41-1 


1-64 


35'4 


357 


36-0 


363 


367 


37'o 


37H 


377 


38-1 


38-5 


38-9 


39'4 


39-8 


40-3 


40-8 


1-66 


35'i 


35'4 


357 


36-0 


36-3 


367 


37'o 


37'4 


37-8 


38-2 


38-6 


39-0 


39'5 


39'9 


40-4 


r68 


34-8 


35'i 


35'4 


357 


36-0 


36-3 


367 


37'i 


37'4 


37-8 


38-3 


387 


39' i 


39-6 


40-1 


170 


34'5 


347 


35'0 


35'4 


357 


36-0 


36-4 


367 


37'i 


37'5 


37'9 


38-4 


38-8 


39'3 


39'8 


172 


34'i 


34'4 


347 


35-o 


35-4 


357 


36-1 


36-4 


36-8 


37'2 


37'6 


38-0 


38-5 


38-9 


39'4 


174 


33-8 


34-i 


34'4 


347 


35'i 


35'4 


357 


36-1 


36-5 


36-9 


37'3 


377 


38-2 


38-6 


39'i 


176 


33-5 


33-8 


34'i 


34'4 


347 


35'i 


35'4 


35-8 


36-2 


36-6 


37' 


37'4 


37-8 


38-3 


38-8 


178 


33'2 


33'5 


33-8 


34'i 


34'4 


34'8 


35'i 


35'5 


35'9 


36-3 


367 


37'i 


37'5 


38-0 


38-5 


i -80 


32-9 


33'2 


33'5 


33-8 


34M 


34'5 


34-8 


35'2 


35-6 


36-0 


36-4 


36-8 


37'2 


377 


38-2 


1-82 


327 


32-9 


33'2 


33*5 


33'9 


34' 2 


34'5 


34'9 


35'3 


357 


36-1 


36-5 


36-9 


37'4 


37'8 


1-84 


32-4 


327 


32-9 


33*2 


33-6 


33'9 


34'2 


34-6 


35'o 


35'4 


35-8 


36-2 


36-6 


37'i 


37'5 


r86 


32-1 


32-4 


327 


33-o 


33'3 


33*6 


33'9 


34'3 


347 


35'i 


35*5 


35'9 


36-3 


36-8 


37'2 


r88 


31-8 


32-1 


32-4 


327 


33'0 


33'3 


337 


34 - o 


34'4 


34'8 


35'2 


35-6 


36*0 


36-5 


37'0 


1-90 


3r6 


31-8 


32-1 


32-4 


327 


33*0 


33*4 


337 


34'i 


34'5 


34'9 


35'3 


357 


36-2 


367 


1-92 


3i-3 


31-6 


31-8 


32-1 


32'4 


32-8 


33'i 


33*5 


33-8 


34'2 


34-6 


35-o 


35'5 


35'9 


36-4 


1-94 


31-0 


3i-3 


3i'6 


3i'9 


32-2 


32-5 


32-8 


33'2 


33-6 


33'9 


34'3 


347 


35'2 


35'6 


36-1 


1-96 


30-8 


31-0 


3i-3 


31-6 


3i-9 


32-2 


32-6 


32-9 


33*3 


337 


34'i 


34*5 


34-9 


35'3 


35-8 


1-98 


30-5 


30-8 


31-1 


3i'3 


317 


32-0 


32'3 


327 


33'0 


33'4 


33-8 


34'2 


34-6 


35'i 


35'5 



Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 

Azimuth is named N or S according to the name of the A and B correction. 



AandB 
Cor- 
rection. 


LATITUDES. 


31 


32 


33 


34 


35 


36 


37 


38 


39 


40 


41 


42 


43 


44 


45 






AZIMUTHS. 






2'00 


3<>'3 


30'5 


30-8 


3I'I 


3i'4 


317 


32'0 


32-4 


32-8 


33'i 


33'5 


33'9 


34'4 


34*8 


35*3 


2-05 


29-6 


29-9 


3 0-2 


30-5 


30-8 


3I-I 


3IH 


3 I'8 


32-1 


32-5 


32-9 


33'3 


337 


34*i 


34-6 


2'IO 


29-1 


29-3 


29-6 


29-9 


30-2 


30-5 


30-8 


3I'I 


31*5 


31-9 


32-3 


327 


33'i 


33*5 


34*o 


2-15 


28-5 


287 


29-0 


2 9 '3 


29-6 


29-9 


3 0-2 


3 0'6 


30-9 


31-3 


31-6 


32-0 


32-5 


32-9 


33'3 


2'20 


27-9 


28-2 


28-5 


28'7 


29-0 


29-3 


29'6 


3 0'0 


3<>'3 


307 


31-1 


31-5 


3i'9 


32-3 


327 


2-25 


27-4 


277 


27-9 


28'2 


28-5 


28-8 


29'I 


29'4 


2 9 '8 


30'i 


30-5 


30-9 


3i'3 


317 


32'2 


2-30 


26-9 


27-1 


27-4 


277 


28-0 


28-3 


28-6 


28-9 


29-2 


29-6 


29-9 


30*3 


307 


3i'i 


31-6 


2'40 


25-9 


26-2 


26-4 


26-7 


27-0 


27-2 


27-6 


27-9 


28-2 


28'5 


28-9 


29-3 


29-7 


30'i 


30-5 


2-50 


25-0 


25*3 


25*5 


25-8 


26-0 


26-3 


26-6 


26-9 


27-2 


27-6 


27-9 


28-3 


28-7 


29-1 


29'5 


2 '60 


24-2 


24-4 


24-6 


24-0 


25-2 


25H 


257 


26'0 


26-3 


267 


27-0 


27-4 


277 


28-1 


28-5 


270 


23*4 


23-6 


23-8 


24-1 


24'3 


24-6 


24-9 


25'2 


25'5 


2 5 '8 


26-1 


26-5 


26-9 


27-2 


27-6 


2'80 


22-6 


22-8 


23-1 


23'3 


23-6 


23-8 


2 4 'I 


24-4 


247 


25-0 


25'3 


257 


26-0 


26-4 


26-8 


2-90 


21-9 


22'I 


22-4 


22-6 


22-8 


23-1 


23'4 


2 3 -6 


23-9 


24-2 


24-6 


24-9 


25-2 


25-6 


.26-0 


3*00 


21-2 


21-5 


217 


21-9 


22'I 


22' 4 


227 


22'9 


23-2 


23-5 


23-8 


24-2 


24'5 


24-9 


25-2 


3'io 


20-6 


20-8 


2I'O 


21-3 


21'5 


217 


22-0 


22'3 


22-5 


22'8 


23-1 


23'5 


2 3 '8 


24-2 


24-5 


3'20 


20'0 


2O*2 


20'4 


20-7 


20'9 


2I'I 


21-4 


21'6 


21-9 


22'2 


22'5 


22'8 


23-1 


23-5 


23-8 


3'3Q 


I9-5 


I9-7 


10-9 


2O'I 


20'3 


20-5 


20'8 


2I'O 


21'3 


21'6 


2I-9 


22'2 


22'5 


22'8 


23-2 


3'4 


l8'9 


19'! 


I9-3 


19-5 


I9-8 


20-0 


20'2 


2O'5 


207 


21'0 


21'; 


21-6 


21-9 


22*2 


22'6 


3-60 


18-0 


18-1 


l8'3 


18-5 


I8 7 


19-0 


I9-2 


19-4 


197 


I9'9 


20-2 


2O'5 


20'8 


2I'I 


21 '4 


3-80 


17-1 


17-2 


I7-4 


17-6 


I 7 -8 


18-0 


18-2 


I8'5 


187 


I9'o 


I9'2 


I9'5 


19-8 


20' I 


20'4 


4-00 


16-3 


16-4 


16-6 


16-8 


I7-0 


17-2 


17*4 


I 7 -6 


17-8 


18-1 


18-3 


18-6 


18-9 


19-2 


I9'5 


4-20 


I5'5 


157 


15-8 


16-0 


I6'2 


16-4 


16-6 


16-8 


17-0 


17*3 


i7'5 


17-8 


18-0 


18-3 


18-6 


4-40 


14-9 


15*0 


I5'2 


I5-3 


I5-5 


157 


i5'9 


16-1 


16-3 


16-5 


16-8 


17-0 


17-3 


i7'5 


17-8 


4-60 


14-2 


14-4 


J 4'5 


147 


I 4 '9 


I5'Q 


15*2 


!5'4 


I5'6 


15-8 


16-1 


16-3 


16-6 


16-8 


17-1 


4-80 


137 


13-8 


14-0 


14-1 


I4'3 


14-4 


14-6 


148 


15-0 


I5'2 


!5'4 


157 


15-9 


I6'2 


i6' 4 


S'oo 


13-1 


13*3 


I3H 


13-6 


137 


i3'9 


14-1 


14-2 


14-4 


14-6 


14-8 


15-1 


I5-3 


I5'5 


15-8 


5'5<> 


I2'0 


I2'I 


I2'2 


12-4 


12-5 


127 


12-8 


13-0 


I3'2 


I3'4 


I3-5 


137 


14-0 


14-2 


*4'4 


6 - oo 


II'O 


II'I 


11*2 


11-4 


"'5 


ir6 


ii-8 


11-9 


I2'I 


12-3 


12-5 


za-6 


I2'8 


I3'0 


I3'3 


6-50 


IO'2 


I0'3 


IO- 4 


10-5 


iO'6 


io-8 


10-9 


II'O 


II'2 


11-4 


11-5 


117 


xi'9 


12 I 


12-3 


7*00 


9'5 


9*6 


97 


9-8 


9-9 


lO'O 


IO'I 


10-3 


10-4 


10 6 


107 


irg 


ii i 


ZX'2 


xx-4 


8-0 


8'3 


8-4 


8'5 


8-6 


87 


8-8 


8-9 


9-0 


9-1 


9*3 


9-4 


9'5 


97 


9-9 


XO'O 


9-0 


7'4 


7'5 


7'5 


7-6 77 


7-8 


7-9 


8-0 


8'i 


8'3 


8' 4 


8'5 


8-6 


8-8 


8-9 


lO'O 


6-7 


6-7 


6-8 


6-9 7-0 


7-0 


7-1 


7-2 


7*3 


7'4 


7'5 


77 


7-8 


7'9 


8-0 


xro 


6-1 


6-1 


6'2 


6-3! 6-3 


6' 4 


6'5 


6-6 


67 


6-8 


6-9 


7-0 


7'i 


7-2 


7'3 


12 -o 


5'6 


5*6 


57 


57 


5-8 


5'9 


6-0 


6-0 


6-i 


6'2 


6-3 


6' 4 


6-5 


6'6 


67 


13-0 


5'i 


5*2 


5'2 


5'3 


5'4 


5 '4 


5'5 


5'6 


57 


57 


5'8 


5'9 


6-0 


6'i 


6-2 


i5'o 

T*7*n 


4'4 

o/1 


4'5 

A *f\ 


4'5 

A *f\ 


4'6 


47 


47 


4-8 


4-8 


4'9 


5'0 


5'o 


5'i 


5'2 
4'6 


5'3 
4*7 


5'4 
4-8 


I/ U 

2O'O 


j y 
3'3 


4 u 

3'4 


4 

3'4 


3*5 


3'5 


3*5 


3-6 


3-6 


37 


37 


3-8 


3'8 


*f v 

3'9 


* / 
4-0 


^ 

4-0 


25-0 


27 


27 


27 


2'8 


2'8 


2'8 


2 -9 


2-9 


2-9 


3'0 


3-0 


3'i 


3'i 


3'2 


3-2 


30-0 


2'2 


2-3 


2-3 


2-3 


2-3 


2-4 


2-4 


2-4 


2'5 


2'5 


2-5 


2'6 


2'6 


27 


27 


40*0 


17 


17 


17 


17 


17 


1-8 


1-8 


i'8 


1-8 


1-9 


1-9 


i -9 


2'0 


2'0 


2'0 


50-0 


i'3 


i '4 


i'4 


i'4 


i '4 


i'4 


i '4 


r*5 


i'5 


1*5 


i'5 


i '5 


1-6 


1-6 


1-6 

I'2 


yo'o 

lOO'O 


I'O 

07 


I'O 

0-7 


I'O 

0-7 


ro 
07 


I'O 

07 


I'O 

0-7 


I'O 

07 


I'O 

07 


i'i 
07 


i'i 
07 


0-8 


0-8 


0-8 


0-8 


0-8 


150-0 


0-4 


0'5 


o*5 


0-5 


0'5 


0-5 


0-5 


0'5 


0'5 


0'5 


0-5 


0'5 


0-5 


0'5 


0'5 


2OO'O 


0-3 


0-3 


0-3 


0-3 


0-3 


0-4 


0-4 


0-4 


0-4 


0-4 


0-4 


0-4 


0-4 


0-4 


0-4 


300-0 


O-2 


0'2 


0'2 


O'2 


O'2 


O'2 


0-2 


O'2 


O'2 


O'2 


0-3 


0-3 


0'3 


0-3 


0'3 


400-0 


O'2 


O'2 


O-2 


0-2 


0'2 


O'2 


0'2 


0'2 


0'2 


O'2 


0'2 


O'2 


O-2 


0-2 


O'2 


800-0 


o-i 


o-i 


O'l 


O'l 


O'l 


O'l 


O'l 


O'l 


o-i 


O'l 


O'l 


O'l 


O'l 


O'l 


O'l 



Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 
Azimuth is named N or S according to the name of the A and B correction. 



A and B 
Cor- 
rection. 


46 


LATITUDES. 


! 
47 


48 


49 


50 


51 


52 


53 


54 


55 


56 57 


58 ! 59 

I 


60 


AZIMUTHS. 


1 








o 


o 


o 


o 








o 


o 


o 





o 


o 





ooo 


90-0 


90-0 


90-0 


90-0 


go'o 


90-0 


90-0 


90-0 


90-0 


90-0 


90-0 


90-0 


90-0 


90-0 


90-0 


oio 


89-6 


89-6 


89-6 


89-6 


89-6 


8 9 -6 


89-6 


897 


8 97 


897 


897 


897 


897 


897 


897 


020 


8 9 -2 


89-2 


89-2 


89-2 


89-3 


89-3 


89-3 


89-3 


8 9 -3 


89-3 


89-4 


89-4 


89-4 


89-4 


89-4 


030 


88-8 


88-8 


88'9 


88'9 


88-9 


88-9 


88'9 


8 9 -0 


8 9 -0 


89-0 


89-0 


89-1 


8 9 -I 


89-1 


89-1 


040 


88-4 


88-4 


88-5 


88'5 


88-5 


88-6 


88-6 


88-6 


88 7 


887 


887 


88-8 


88-8 


88-8 


88-9 


050 


88-0 


88-0 


88-i 


88-1 


88-2 


88-2 


88-2 


88-3 


88'3 


88-4 


88-4 


88-4 


88-5 


88-5 


88-6 


060 


87-6 


877 


877 


877 


87-8 


87-8 


87-9 


87-9 


88-0 


88-0 


88-1 


88-1 


88-2 


88-2 


88-3 


070 


87-2 


87-3 


87-3 


87*4 


87'4 


87-5 


87-5 


87-6 


87-6 


877 


87-8 


87-8 


87-9 


87-9 


88-0 


080 


86-8 


86-9 


86-9 


87*0 


87-1 


87-1 


87-2 


87-2 


87-3 


87-4 


87-4 


87-5 


87-6 


87-6 


877 


OQO 


86-4 


86-5 


86-6 


86-6 


867 


86-8 


86-8 


86-9 


87-0 


87-0 


87-1 


87-2 


87-3 


87-3 


87-4 


100 


86-0 


86-1 


86-2 


86-2 


86-3 


86-4 


86-5 


86-6 


86-6 


867 


86-8 


86-9 


87-0 


87-1 


87-1 


no 


85-6 


857 


85-8 


85*9 


86-0 


86-0 


86-1 


86-2 


86-3 


86-4 


86-5 


86-6 


867 


86-8 


86-9 


'I2O 


85-2 


85-3 


85H 


85-5 


85-6 


857 


85-8 


85-9 


86-0 


86-1 


86-2 


86-3 


86-4 


86-5 


86-6 


130 


84-8 


84-9 


85-0 


85-1 


85-2 


85-3 


85-4 


85-5 


85-6 


857 


85-8 


86-0 


86-1 


86-2 


86-3 


140 


84-4 


84-5 


84-6 


84-8 


84-9 


85-0 


85-1 


85-2 


85-3 


85-4 


85-5 


85-6 


8 5 '8 


85-9 


86-0 


'ISO 


84-1 


84-2 


84-3 


84-4 


84-5 


84-6 


847 


84-8 


85-0 


85-1 


85-2 


85-3 


85-5 


85-6 


857 


160 


837 


83-8 


83*9 


84-0 


84-1 


84-3 


84H 


84-5 


84-6 


84-8 


84-9 


85-0 


85-2 


85-3 


85'4 


170 


83-3 


83H 


83-5 


83-6 


83-8 


83-9 


84-0 


84-2 


843 


84-4 


84-6 


847 


84-9 


85-0 


85-1 


180 


82-9 


83-0 


83-1 


833 


83H 


83-5 


837 


83-8 


84-0 


84-1 


84-3 


84-4 


84-6 


847 


84-9 


190 


82-5 


82-6 


82-8 


82-9 


83-0 


83-2 


83-3 


83-5 


83-6 


83-8 


83-9 


84-1 


84-3 


84'4 


84-6 


200 


82-1 


82-2 


82-4 


82-5 


827 


82-8 


83-0 


83-1 


83-3 


83-5 


83-6 


83-8 


84-0 


84-1 


843 


'210 


817 


81-8 


82-0 


82-2 


82-3 


82-5 


82-6 


82-8 


83-0 


83-1 


83-3 


83-5 


837 


83-8 


84-0 


'22O 


81-3 


81-5 


81-6 


8r8 


82-0 


82-1 


82-3 


82-5 


82-6 


82-8 


83-0 


83-2 


83H 


83-5 


837 


230 


80-9 


8ri 


8r 3 


81-4 


8r6 


8r8 


81-9 


82-1 


82-3 


82-5 


827 


82-9 


83-1 


83-2 


83-4 


240 


80-5 


807 


80-9 


8ri 


8l'2 


81-4 


8r6 


8r8 


82-0 


82-2 


82-4 


82-6 


82-8 


83-0 


83-2 


250 


80- 1 


80-3 


80-5 


807 


80-9 


8ri 


81-2 


81-4 


81-6 


8r8 


82-0 


82-2 


82-5 


827 


82-9 


260 


79-8 


79-9 


80-1 


80-3 


80-5 


807 


80-9 


81-1 


81-3 


81-5 


817 


81-9 


82-2 


82-4 


82-6 


270 


79'4 


79-6 


79-8 


80-0 


80-2 


8o- 4 


80-6 


80-8 


8ro 


81-2 


81-4 


81-6 


81-9 


82-1 


82-3 


280 


79-0 


79*2 


79'4 


79-6 


79-8 


80-0 


80-2 


80-4 


807 


80-9 


8ri 


81-3 


8r6 


8r8 


82-0 


290 


78-6 


78-8 


79-0 


79-2 


79'4 


797 


79-9 


80-1 


80-3 


80-6 


80-8 


8rc 


81-3 


81-5 


817 


3 00 


78-2 


78-4 


78-6 


78-9 


79-1 


79'3 


79'5 


79-8 


80-0 


.80-2 


80-5 


807 


81-0 


81-2 


81-5 


310 


77'8 


78-1 


78-3 


78-5 


787 


79-0 


79-2 


79'4 


797 


79'9 


80-2 


80-4 


807 


80-9 


81-2 


3 20 


77'5 


777 


77'9 


78-1 


78-4 


78-6 


78-9 


79-1 


79'3 


79-6 


79'9 


80- 1 


80-4 


80-6 


80-9 


330 


77-1 


77'3 


77'5 


77'8 


78-0 


78'3 


78-5 


78-8 


79-0 


79'3 


79*5 


79-8 


80-1 


80-4 


80-6 


34> 


767 


76-9 


77-2 


77'4 


777 


77'9 


78-2 


78-4 


787 


79-0 


79-2 


79'5 


79-8 


80- 1 


80-4 


'350 


76-3 


76-6 


76-8 


77-1 


77'3 


77-6 


77-8 


78-1 


78-4 


78-6 


78-9 


79-2 


79'5 


79-8 


80- 1 


360 


76-0 


76-2 


76-5 


767 


77-0 


77-2 


77'5 


77-8 


78-1 


78-3 


78-6 


78-9 


79-2 


79'5 


79-8 


III 


75-6 
75'2 


75-8 
75'5 


76-1 
757 


76-4 
76^0 


76-6 
76-3 


76-9 
76-6 


77*2 
76-8 


77'4 
77-1 


777 
77'4 


78-0 
777 


78-3 
78-0 


78-6 
78-3 


78-9 
78-6 


79-2 
78-9 


79'5 
79-2 


390 


74-8 


75'i 


75'4 


75-6 


75'9 


76-2 


76-5 


76-8 


77-1 


77'4 


777 


78-0 


78-3 


78-6 


79-0 


4 00 


74*5 


747 


75'o 


75'3 


75-6 


75*9 


76-2 


76-5 


76-8 


77-1 


77'4 


777 


78-0 


78-4 


787 


4 IO 


74'i 


74'4 


747 


74'9 


75'2 


75'5 


75-8 


76-1 


76-5 


76-8 


77-1 


77'4 


777 


78-1 


78-4 


420 


737 


74-0 


74'3 


74-6 


74'9 


75'2 


75'5 


75-8 


76-1 


76-5 


76-8 


77-1 


77'5 


77-8 


78-1 


430 


73'4 


737 


73-9 


74'2 


74'5 


74'9 


75'2 


75'5 


75'8 


76-1 


76-5 


76-8 


77'2 


77'5 


77'9 


440 


73'<> 


73'3 


73'6 


73'9 


74*2 


74'5 


74-8 


75'2 


75*5 


75-8 


76*2 


76'5 


76-9 


77*2 


77-6 


450 


72-6 


72-9 


73*2 


73'6 


73*9 


74'2 


74'5 


74-8 


75'2 


75'5 


75'9 


76-2 


76-6 


77-0 


77*3 


460 


72-3 


72-6 


72-9 


73-2 


73*5 


73'9 


74-2 


74-5 


74'9 


75'2 


75-6 


75'9 


76-3 


767 


77-0 


470 


71-9 


72*2 


72-5 


72-9 


73*2 


73'5 


73'9 


74*2 


74-6 


74-9 


75'3 


75-6 


76-0 


76-4 


76-8 


4 80 


71-6 


71-9 


72-2 


72'5 


72-9 


73'2 


73'5 


73'9 


74'2 


74-6 


75'0 


75'3 


757 


76-1 


76-5 


490 


71-2 


7i'5 


71-8 


72-2 


72-5 


72-9 


73'2 


73'6 


73'9 


74'3 


747 


75'i 


75'4 


75-8 


76-2 




47 



Table C. 
AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 

Azimuth is named N or S according to the name of the A and B correction. 



AandB 
Cor- 
rection. 


LATITUDES, 


46 


47 


48 


49 


50 


51 


52 53 

i 


54 


55 


58 


57 


58 


69 


60 


AZIMUTHS. 


' 








o 


o 


o 


o 


i 








o 








o 








500 


70-8 


71-2 


71-5 


7I' 


72-2 


72-5 


72'S 


73'2 


73-6 


74-0 


74'4 


74*8 


75'2 


75-6 


76*0 


510 


70-5 


70-8 


7 I-2 


7 1 '" 


7 I-8 


72-2 


72-6 


72-5 


73'3 


737 


74-1 


74*5 


74'9 


75'3 


757 


520 


70-1 


7'5 


70-8 


71-2 


7*5 


71-9 


72-2 


72-e 


73'Q 


73'4 


73*8 


74-2 


74-6 


75' 


75*4 


530 


69-8 


70-1 


7'5 


70-8 


71-2 


71-6 


71-9 


72-3 


727 


73'i 


73'5 


73'9 


74'3 


747 


75'2 


540 


69-4 


69-8 


70-1 


70'5 


70-9 


71-2 


71-6 


72'C 


72-4 


72-8 


73'2 


73*6 


74-0 


74'5 


74'9 


550 


69-1 


69-4 


69-8 


70-2 


70-5 


70-9 


71*3 


717 


72-1 


72'5 


72-9 


73'3 


73'8 


74-2 


74-6 


i '560 


687 


69-1 


69-5 


69-8 


70-2 


70-6 


71-0 


71-4 


71-8 


72-2 


72-6 


73-0 


73'5 


73'9 


74'4 


570 


68-4 


68-8 


69-1! 69-5 


69-9 


70-3 


707 


71-1 


7i'5 


71-9 


72-3 


72-8 


73-2 


73-6 


74-1 


; -580 


68-1 


68-4 


68-8 


69-2 


69-6 


69-9 


70-3 


70-8 


71-2 


7 x;6 


72-0 






73'4 


73-8 


590 


677 


68-1 


68-5 


68-8 


69-2 


69-6 


70-0 


70-5 


70-9 




717 


72-2 


72-6 




73-6 


600 


67-4 


677 


68-1 


68-5 


68-9 


69-3 


697 


70-1 


70-6 


71-0 


7i'5 


71-9 


72-4 


72-8 


73'3 


610 


67-0 


67-4 


67-8 


68-2 


68-6 


69-0 


69-4 


69-8 




707 


71-2 


71-6 


72-1 


72-6 


73-0 


'620 


667 


67-1 


67-5 


67-9 


68-3 


687 




69-5 


70-1 


70-4 


70-9 




71-8 


72-3 


72-8 


630 


66-4 


667 


67-1 


67*5 


68-0 


68-4 


68-8 


69-2 


697 


70-1 


70-6 


71-1 


7 1 '5 


72-0 




' "640 


66-0 


66-4 


66-8 


67-2 


67-6 


68-1 


68-5 


68-9 


69-4 


69-8 




70-8 




71-8 


72-3 


650 


657 


66-1 


66-5 


66-9 


67-3 


67-8 


68-2 


68-6 


69-1 


69-6 


70-0 


7 o- 5 


71-0 


7i-5 


72-0 


660 


65-4 


65-8 


66-2 


66-6 


67-0 


67-4 


67-9 


68-3 


68-8 


69-3 


697 


70-2 


707 


71-2 


717 


670 


65-0 


65-4 


65-9 


66-3 


667 


67-1 


67-6 


68-0 


68-5 


69-0 


69-5 


70-0 


7'5 


71-0 




680 


647 


65-1 


65-5 


66-0 


66-4 


66-8 


67-3 


677 


68-2 


687 


69-2 


697 


70-2 


707 


71-2 


690 


64-4 


64-8 


65-2 


65-6 


66-1 


66-5 


67-0 


67-4 


67-9 


68-4 


68-9 


69-4 


69-9 


70-4 


71-0 


'700 - 


64-1 


64-5 


64-9 


65-3 


65-8 


66-2 


667 


67-2 


67-6 


68-1 


68-6 


69-1 


69-6 


70-2 


707 


7 10 


637 


64-2 


64-6 


65-0 


65-5 


65-9 


66-4 


66-9 


67-3 


67-8 


68-3 


68-9 


69-4 


69-9 


70-5 


720 




63-8 




647 


65-2 


65-6 


66-1 


66-6 


67-1 


67-6 


68-1 


68-6 


69-1 


697 


70-2 


.730 


63-1 


63-5 


64-0 


64-4 


64-9 


6 5 ;3 


65-8 


66-3 


66-8 


67-3 


67-8 


68-3 


68-9 


69-4 


69-9 


740 


62-8 




637 


64-1 


64-6 




65-5 


66-0 


66-5 


67*0 


67-5 


68-0 


68-6 


69-1 


697 


750 


62 : 5 


62*9 


63-4 


63-8 


64*3 


647 


65-2 


657 


66-2 


667 


67-2 


67-8 


68-3 


68-9 


69-4 


-760 


62-2 


62-6 


63-0 


63-5 


64-0 


64-4 


64-9 


65-4 


65-9 


66-4 


67-0 


67-5 


68-1 


68-6 


69-2 


, ,770 


61-9 


62-3 


627 


63-2 


637 


64-1 


64-6 


65-1 


65-6 


66-2 


667 


67-2 


6 7 : 8 


68-4 


68-9 


780 


61-5 


62'O 


62-4 


62-9 




3-9 


64-3 


64-9 


65-4 


65-9 


66-4 


67-0 




68-1 


687 


790 


61-2 


617 


62-1 


62-6 


63-1 


63-6 


64' i 


64-6 


65-1 


65-6 


66-2 


667 


67-3 


67-9 


68-4 


.800 


60-9 


61-4 


61-8 


62-3 


62-8 


63-3 


63-8 


64-3 


64-8 


65-4 


65-9 


66-5 


67-0 


67-6 


68-2 


"810 


60-6 


61-1 


61-5 


62-0 


62-5 


63-0 


63-5 


64-0 


64-5 




65-6 


66-2 


66-8 


67-4 


68-0 


-820 


60-3 


60-8 


61-2 


617 


62-2 


627 


63-2 


637 




64-8 




65-9 


66-5 


67-1 


677 


830 


60-0 


60-5 


6i'0 


61-4 


61-9 


62-4 


62-9 


63-5 


64-0 


64-5 


65-1 


657 


66-3 


66-9 


67-5 


"840 


597 


60-2 


607 


0X-I 


61-6 


62-1 


627 


63-2 


637 


64-3 


64-9 


65-4 


66-0 


66-6 


67-2 


850 


59'4 


59'9 


60-4 


60-9 


61-3 


61-9 


62-4 


62-9 


63-5 


64-0 


64-6 


65-2 


65-8 


66-4 


67-0 


.860 






60- 1 


60-6 


61-1 


61-6 


62-1 


62-6 


63-2 


637 


64*3 


64-9 


65*5 


66-1 


667 


870 


58'9 


59'3 


59'8 


60-3 


60-8 


61-3 


61-8 


62-4 


62*9 


63-5 


64-1 


64-6 


65-2 


65-9 


66-5 


880 


58-6 


59' 


59*5 


60-0 


60-5 


6i'O 


61-6 


62-1 


62-6 


63-2 


63-8 


64-4 


65-0 


65*6 


66-3 


890 


58-3 


587 




597 


60-2 


607 


61-3 


61-8 


62*4 


63-0 


63-5 


64-1 


64-8 


65-4 


66-0 


900 


58-0 


58'5 


58-9 


59'4 


60-0 


60-5 


61-0 


61-6 


62-1 


627 


63-3 


63-9 


64*5 


65-1 


6 5 '8 


910 


577 


58-2 


587 


59*2 


597 


60-2 


607 


61-3 


61-9 


62-4 


63-0 


63-6 


64-3 


64-9 


65-5 


920 


57*4 


57'9 


58-4 




59'4 


59-9 


60-5 


61-0 


61-6 


62-2 


62-8 


63-4 


64-0 


64-6 


65-3 


930 


57' 1 




58-1 


58-6 




597 


60-2 


60-8 


61-3 


61-9 


62-5 


63-1 


63-8 


64*4 


65-1 


940 




57'3 


57-8 


58-3 


58-9 


59'4 


59'9 


60-5 


6ri 


617 


62-3 


62-9 


63*5 


64-2 


64-8 


'950 
960 
970 


56-6 

56-3 
56-0 


56-8 
56-5 


57-6 
57'3 


58-1 
57'8 
57*5 


58-6 
58-3 
58-1 


58-9 
58-6 


597 
59'4 


60-2 
60-0 
597 


60-8 
60-6 
60-3 


61-4 
61-2 
60-9 


62-0 
61-8 
61-5 


62-6 
62-4 
62-2 


63'3 
63-0 
62-8 


63-9 
637 
63-5 


64-6 
64-4 
64-1 


980 
990 


55-8 
55'5 


56-2 
56-0 


567 
56-5 


57'3 


57-8 
57'5 


58-3 
58-1 


58-6 


59'5 
59'2 


60- 1 


607 
60-4 


61-3 
61-0 


617 


62*6 
62-3 


63-2 
63*0 


63-9 
637 



Table C. 
AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION 

Azimuth is named N or S according to the name of the A and B correction. 



Aaod B 
Cor- 
rection. 


LATITUDES. 


46 


47 


48 


49 


50 


51 


52 ! 53 


54 


55 


56 


57 58 


59 


60 


AZIMUTHS. 


/ 














= 


o 


O : O 


1 


o 


o 











o 


I '00 


55'2 


557 


56-2 


567 


57'3 


57-8 


58H 


59'0 


59-6 


60'2 


60-8 


6r 4 


62-1 


627 


63'4 


I'O2 


547 


55*2 


557 


56-2 


567 


57'3 


57'9 


58-5 


59'i 


597 


60'3 


60'9 


6r6 


62-3 


63-0 


I '04 


54'2 


547 


55'2 


557 


56-2 


56-8 


57'4 


58-o 


58-6 


59'2 


59-8 


60-5 


6ri 


6r8 


62-5 


i'o6 


53'6 


54'i 


547 


55'2 


557 


56-3 


56-9 


57'5 


58-1 


587 


59'3 


60'0 


607 


61-4 


62-1 


I -08 


53'i 


53-6 


54'i 


547 


55*2 


55-8 


56-4 


57'o 


57'6 


58-2 


58-9 


59*5 


60-2 


60-9 


6r6 


I'lO 


52-6 


53'i 


53'6 


54'2 


547 


55'3 


55'9 


56-5 


57'i 


57'8 


58-4 


59'i 


59-8 


60-5 


61-2 


ri2 


52-1 


52-6 


53'2 


537 


54'2 


54'8 


55'4 


56-0 


56-6 


57'3 


57'9 


58-6 


59*3 


60-0 


60-8 


1-14 


5i-6 


52-1 


527 


53'2 


53-8 


54'3 


54'9 


55'5 


56-2 


56-8 


57'5 


58-2 


58-9 


59'6 


60-3 


1-16 


5i'i 


517 


52-2 


527 


53'3 


53'9 


54'5 


55'i 


557 


56-4 


57' 


577 


58-4 


59'i 


59'9 


ri8 


507 


5i'2 


5i7 


52-3 


52-8 


53'4 


54'0 


54'6 


55'3 


55*9 


56-6 


57'3 


58-0 


587 


59'5 


I'2O 


50-2 


507 


51-2 


51-8 


52-4 


52-9 


53*5 


54'2 


54*8 


55'5 


56*1 


56-8 


57'5 


58-3 


59'o 


I '22 


497 


50-2 


50-8 


5i'3 


5i-9 


52-5 


53'i 


537 


54*4 


55*0 


557 


56-4 


57'i 


57'9 


58-6 


I-2 4 


49'3 


49 -8 


50-3 


50-9 


5i'4 


52-0 


52-6 


53'3 


53*9 


54'6 


55'3 


56-0 


567 


57'4 


58-2 


1-26 


48-8 


49'3 


49'9 


50*4 


51-0 


5r6 


52-2 


52-8 


53*5 


54'i 


54'8 


55'5 


56-3 


57' 


57'8 


1-28 


48-4 


48-9 


49'4 


50-0 


50-6 


5i'i 


51-8 


52-4 


53'0 


537 


54'4 


55'i 


55'9 


56-6 


57'4 


I-30 


47 '9 


48-4 


49-0 


49'5 


50-1 


507 


5i'3 


52-0 


52-6 


53'3 


54' 


547 


55'4 


56-2 


57'o 


I'32 


47'5 


48-0 


48-5 


49-1 


497 


50-3 


50*9 


5^5 


52-2 


52-9 


53-6 


54'3 


55'0 


55-8 


56-6 


i '34 


47-1 


47'6 


48-1 


487 


49'3 


49'9 


50*5 


5i'i 


51-8 


52'5 


53'2 


53*9 


54-6 


55*4 


56-2 


1-36 


46-6 


47-2 


477 


48-3 


48-8 


49'4 


50-1 


507 


5i-4 


52-0 


527 


53'5 


54*2 


55'o 


55-8 


1-38 


46*2 


467 


47'3 


47'8 


48-4 


49-0 


49-6 


50-3 


51-0 


51-6 


52-3 


53'i 


53-8 


54-6 


55'4 


r 4 o 


45'8 


46-3 


46-9 


47*4 


48-0 


48-6 


49'2 


49'9 


50-5 


51-2 


5I-9 


527 


53'4 


54*2 


55*0 


1-42 


45'4 


45-9 


46-5 


47-0 


47-6 


48-2 


48-8 


49*5 


50-1 


50-8 


5i'5 


52-3 


53'o 


53-8 


54'6 


i '44 


45'0 


45'5 


46-1 


46-6 


47-2 


47'8 


48-4 


49-1 


49-8 


50-4 


51-2 


5i'9 


527 


53'4 


54'2 


1-46 


44-6 


45'i 


457 


46-2 


46-8 


47'4 


48-0 


487 


49'4 


50-1 


50-8 


5^5 


52-3 


53'i 


53'9 


l- 4 8 


44-2 


447 


45'3 


45'8 


46-4 


47-0 


477 


48-3 


49-0 


497 


50-4 


5i'i 


5i-9 


527 


53'5 


1-50 


43-8 


44'3 


44'9 


45*5 


46-0 


467 


47'3 


479 


48-6 


49'3 


50-0 


50-8 


5^5 


52-3 


S3'* 


1-52 


43'4 


44-0 


44'5 


45'i 


457 


46-3 


46-9 


47'5 


48-2 


48-9 


49-6 


50-4 


5i'i 


5i-9 


52-8 


I '54 


43'i 


43-6 


44-1 


447 


45'3 


45*9 


46-5 


47-2 


47-8 


48-5 


493 


50-0 


50-8 


5i-6 


52-4 


1-56 


427 


43'2 


43'8 


44*3 


44 '9 


45'5 


46-2 


46-8 


47*5 


48-2 


48-9 


49-6 


50-4 


51-2 


52-0 


1-58 


42-3 


42-9 


43'4 


44-0 


44-6 


45*2 


45-8 


46-4 


47-1 


47-8 


48-5 


49*3 


50-1 


50-9 


517 


I -60 


42-0 


42-5 


43*o 


43-6 


44-2 


44-8 


45'4 


46-1 


46-8 


47'5 


48-2 


48-9 


497 


50-5 


5i'3 


1-62 


41-6 


42-1 


427 


43'3 


43'8 


44'4 


45'i 


457 


46-4 


47-1 


47-8 


48-6 


49'4 


50-2 


51-0 


r6 4 


4i'3 


41-8 


42-3 


429 


43*5 


44-1 


447 


45'4 


46-1 


46-8 


47'5 


48-2 


49'o 


49-8 


50-6 


1-66 


40-9 


4i'5 


42-0 


42*6 


43'i 


437 


44'4 


45'o 


457 


46-4 


47-1 


47 '9 


487 


49'5 


50-3 


1-68 


40*6 


41-1 


417 


42-2 


42-8 


43*4 


44 -o 


447 


45'4 


46-1 


46-8 


47'5 


48-3 


49' ! 


5O'o 


170 


40-3 


40-8 


4i'3 


41-9 


42-5 


43'i 


437 


44'3 


45'0 


457 


46-4 


47-2 


48-0 


48-8 


49-6 


172 


39'9 


40-4 


41-0 


4i'5 


42-1 


427 


43'4 


44-0 


447 


45'4 


46*1 


46-9 


477 


48-5 


49'3 


i'74 


39-6 


40*1 


407 


41-2 


41-8 


42-4 


43'o 


437 


44'4 


45'i 


45-8 


46*5 


47'3 


48-1 


49'0 


176 


39'3 


39'8 


40-3 


40-9 


4i'5 


42-1 


427 


43*4 


44-0 


447 


45'5 


46-2 


47-0 


47-8 


487 


178 


39-0 


39'5 


40-0 


4O'6 


41-2 


41-8 


42-4 


43' 


437 


44*4 


45'i 


.45'9 


467 


47'5 


48-3 


i -80 


387 


39'2 


397 


403 


40-8 


41-4 


42-1 


427 


43'4 


44-1 


44-8 


45'6 


46-4 


47'2 


48-0 


1-82 


38-3 


38-9 


39'4 


39'9 


40-5 


41-1 


417 


42-4 


43'i 


43-8 


44'5 


45'3 


46-0 


46-9 


477 


1-84 


38-0 


38-6 


39'i 


39-6 


40-2 


40-8 


41-4 


42-1 


42-8 


43'5 


44-2 


44'9 


457 


46-5 


47 '4 


1-86 


377 


38-2 


38-8 


39'3 


39'9 


40-5 


41-1 


41-8 


42-4 


43'i 


43'9 


44-6 


45'4 


46-2 


47-1 


1-88 


37'4 


38-0 


38-5 


39-0 


39-6 


40-2 


40-8 


4*'5 


42-1 


42-8 


43'6 


44'3 


45-i 


45'9 


46-8 


i '90 


37'i 


377 


38-2 


387 


39'3 


39'9 


40-5 


41-2 


41-8 


42'5 


43'3 


44-0 


44*8 


45-6 


46-5 


1-92 


36-9 


37'4 


37'9 


38-4 


39-0 


39-6 


40-2 


40-9 


4i'5 


42-2 


43-o 


437 


44'5 


45'3 


46-2 


1-94 


36-6 


37' 1 


37-6 


38-2 


387 


39'3 


39'9 


40-6 


41-2 


41-9 


427 


43'4 


44-2 


45'0 


45'9 


r 9 6 


36-3 


36-8 


37'3 


37'9 


38-4 


39-0 


39-6 


4'3 


41-0 


417 


42-4 


43'i 


43'9 


447 


45'6 


1-98 


36-0 


36-5 


37' 


37-6 


38-2 


387 


39'4 


40-0 


407 


41-4 


42-1 


42-8 


43'6 


44'4J 45'3 



49 



Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 
Azimuth is named N or S according to the name of the A and B correction. 



A and B 
Cor- 
rection. 


LATITUDES. 


46 


47 


48 


49 


50 


51 52 53 


54 


55 


56 


57 





59 


60 3 


f 




AZIMUTHS. 












2'OO 


357 


36-2 


36-8 


37*3 


37'9 


38-5 


39'I 


397 


40-4 


4I'I 


41-8 


4 2-6 


43'3 


44-2 


45'0 


2-05 


35*i 


35-6 


36-1 


36-6 


37'2 


37'8 


3 8' 4 


39-0 


397 


40-4 


4 I'I 


4 r8 


42-6 


43'4 


44'3 


2'IO 


34'4 


34'9 


35'4 


36-0 


36'5 


37'i 


377 


38-4 


39*0 


397 


40-4 


41'2 


41-9 


42-8 


43'6 


2-15 


33-8 


34'3 


34'8 


35*3 


35'9 


36-5 


37'i 


377 


38-4 


39-0 


39'8 


40-5 


4*'3 


42-1 


42-9 


2'20 


33'2 


337 


34'2 


347 


35'3 


35-8 


36-4 


37' 1 


377 


38-4 


39' i 


39'8 


40-6 


41-4 


42'3 


2-25 


32-6 


33'i 


33-6 


34' i 


347 


35'2 


35'8 


36-4 


37*i 


37-8 


38-5 


39'2 


40-0 


40-8 


4 I'6 


2-30 


32-0 


32-5 


33'0 


33'5 


34' i 


34'6 


35*2 


35*8 


36-5 


37'2 


37'9 


38-6 


39*4 


40-2 


41-0 


2-40 


31-0 


3i-4 


3i-9 


32*4 


33' 


33'5 


34'i 


347 


35*3 


36-0 


367 


37'4 


38*2 


39-0 


39-8 


2-50 


29-9 


30-4 


30-9 


3i'4 


31*9 


32-4 


33-o 


33'6 


34'2 


34'9 


35-6 


36-3 


37' 


37'8 


387 


2*60 


29-0 


29-4 


29-9 


30-4 


30-9 


31-4 


32-0 


32-6 


33'2 


33'8 


34'5 


35*2 


36-0 


36-8 


37'6 


270 


28-1 


28-5 


29-0 


29-4 


30-0 


30-5 


31-0 


3 r6 


32-2 


32-9 


33-5 


34'2 


35-o 


357 


36-5 


2-80 


27-2 


27-6 


28-1 


28-6 


29-1 


29-6 


30-1 


307 


3i'3 


3i'9 


32-6 


33'3 


34' 


347 


35'5 


2-90 


26-4 


26-8 


27'3 


277 


28-2 


287 


29'3 


29-8 


30'4 


31-0 


317 


32-3 


33'i 


33-8 


34-6 


3-00 
3-10 


25-6 
24-9 


26-0 
25'3 


26-5 
257 


26-9 
26-2 


2 7'4 
26-6 


27-9 
27-1 


28-4 
277 


29-0 
28-2 


29-6 
28-8 


30-2 
29-4 


30-8 
30-0 


3i'5 
30-6 


32-2 
3i-3 


32-9 
32-1 


337 
32-8 


3-20 


24-2 


24-6 


25-0 


25*5 


25-9 


26-4 


26-9 


27-4 


28-0 


28-6 


29-2 


29-8 


30'5 


31-2 


32-0 


3-30 


23-6 


24-0 


24-4 


24-8 


25-2 


257 


26-2 


267 


27-3 


27-8 


28-5 


29-1 


29-8 


30-5 


31-2 


3'4 


22-9 


23'3 


237 


24-1 


24-6 


25*0 


25-5 


26-0 


26-6 


27-1 


277 


28-4 


29-0 


297 


30*5 


3'6o 


21-8 


22'2 


22-5 


22-9 


23H 


23-8 


24-3 


24-8 


25*3 


25-8 


26-4 


27-0 


277 


28-3 


29-1 


3-80 


20'7 


2I'I 


21-5 


21-9 


22-3 


227 


23-1 


23-6 


24-1 


24-6 


25-2 


25-8 


26-4 


27-1 


27-8 


4-00 


19-8 


2O'I 


20-5 


20-9 


21-3 


217 


22'I 


22-6 


23-0 


23-6 


24-1 


247 


25-3 


25'9 


26-6 


4-20 


18-9 


19-2 


19*6 


19-9 


2O'3 


20-7 


2I'I 


21-6 


22'I 


22-5 


23-1 


23-6 


24-2 


24-8 


24*5 


4-40 


18-1 


18-4 


18-8 


19*1 


19-5 


19-9 


20 3 


207 


2I'I 


21-6 


22'I 


227 


23-2 


23-8 


24-4 


4-60 


17-4 


177 


18-0 


18-3 


187 


19-1 


19-4 


19-9 


203 


20'8 


21*2 


21'8 


22'3 


22'9 


23'5 


4-80 


167 


I7-0 


I7-3 


17-6 


18-0 


18-3 


I8 7 


I9'I 


I9-5 


2O'O 


20'4 


20'9 


215 


22-0 


22-6 


5-00 


16-1 


I6'3 


i6'6 


17-0 


i7'3 


17-6 


18-0 


I8'4 


18-8 


I9-2 


197 


20'2 


207 


21-2 


21'8 


5-50 


14-7 


14-9 


I5'2 


i5'5 


15-8 


16-1 


16-5 


16-8 


17-2 


I 7 -6 


18-0 


18-5 


i8'9 


I9'4 


2O'O 


6'oo 


I3-5 


137 


14-0 


H'3 I4'5 


14-8 


I5'i 


15'5 


15-8 


16-2 


16-6 


17-0 


I7'5 


I7'9 


18-4 


6-50 


12-5 


127 


12-9 


i3'2j i3'5 


137 


14-0 


14-3 


147 


15-0 


i5'4 


I5'8 


16-2 


16-6 


17-1 


7-00 


n-6 


i r8 


I2'I 


12-3 


12-5 


I2'8 


13*1 


I3'4 


137 


14-0 


I4'3 


H7 


iyi 


I5-5 


I5-9 


8-0 


IO'2 


10-4 


10-6 


10-8 


XI'O 


lit 


ii'5 


117 


I2'O 


12-3 


I2'6 


12-9 


I3'3 


13-6 


14-0 


9-0 


9'I 


9'3 


9'4 


9-6 


9-8 


IO'O 


IO'2 


10-5 


107 


II'O 


11*2 


11-5 


ii-8 


I2'2 


12-5 


IO'O 


C'2 


8'3 


8'5 


87 


8-8 


9-0 


9-2 


9'4 


97 


9*9 


IO'I 


10-4 


107 


II'O 


11-3 


II'O 


7'5 


7-6 


77 


7*9 


8-0 


8-2 


8' 4 


8-6 


8-8 


9-0 


9-2 


9'5 


97 


IO'O 


10-3 


I2'O 


6-8 


7-0 


7-1 


7-2 


7*4 


7'5 


77 


7'9 


8'i 


8-3 


8-5 


87 


8-9 


9-2 


9'5 


13-0 


6-3 


6-4 


6-6 


67 


6-8 


7-0 


f 


7'3 


7'5 


7-6 


7-8 


8-0 


8'3 


8'5 


87 


I 5 -0 


5*5 


5'6 


57 


5'8 


5'9 


6-0 


6'2 


6'3 


6'5 


6'6 


6-8 


7-0 


7-2 


7*4 


7'6 


I7-0 


4-8 


4'9 


5'0 


5'i 


5-2 


5'3 


5'5 


5-6 


57 


5*9 


6-0 


6'2 


6'3 


6'5 


67 


20'0 


4' i 


4-2 


4'3 


4'4 


4*4 


4'5 


4-6 


47 


4'9 


5'0 


5'i 


5*2 


5'4 


5'5 


57 


25-0 


3*3 


3'4 


3'4 


3'5 


3-6 


3'6 


37 


3'8 


3*9 


4-0 


4'i 


4-2 


4*3 


44 


4-6 


30-0 


27 


2-8 


2-9 


2-9 


3-0 


3-0 


3'i 


3-2 


3'2 


3'3 


3'4 


3'5 


3'6 


37 


3'8 


40-O 


2'I 


2-1 


2'I 


2'2 


2'2 


2-3 


2-3 


2'4 


2-4 


2-5 


2'6 


2'6 


27 


2'8 


2-9 


50-0 


1-6 


17 


17 


17 


1-8 


1-8 


1-9 


i -9 


i -9 


2'O 


2'0 


2'I 


2'2 


2'2 


2-3 


7O'O 


ra 

_.c 


I'2 
_.o 


I'2 


1*2 


1*3 


i'3 


i'3 


i '4 

IT *r\ 


1*4 

T *f\ 


i'4 

I/N 


i'5 

I'd 


i'5 


i'5 


i'6 


1-6 


100*0 
150-0 


O o 
0'5 


O o 

0-6 


O'9 

0-6 


'9 
0-6 


o'9 
0-6 


0-9 
0-6 


o'g 
0-6 


i O 

0-6 


X w 

0-6 


O 

07 


Q 

07 


07 


07 


07 


0-8 


20O'0 


'4 


0-4 


0-4 


0-4 


0-4 


P*5 


0'5 


o'5 


o'5 


0'5 


o'5 


0'5 


0'5 


0-6 


0-6 


30O-O 


o*' 


Q'3 


0-3 


0-3 


0-3 


0-3 


0'3 


0-3 


0-3 


0-3 


0-3 


0-4 


0-4 


0-4 


0-4 


40O-0 


O'2 


*O'2 


0'2 


0'2 


0'2 


0'2 


O'2 


0'2 


O'2 


0'2 


0-3 


0-3 


0'3 


0-3 


0-3 


800-0 


O'l 


O'l 


o-i 


O'l 


O'l 


O'l 


O'l 


O'l 


O'l 


O'l 


0*1 


O'l 


O'l 


O'l 


O'l 



4 Azimuth 



fiO 



Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 

Azimuth is named N or S according to the name of the A and B correction. 



AandB 
Cor- 
rection. 


LATITUDES. 


61 


62 


63 


64 


65 


86 


67 


68 


89 


69* 


70 


70J 


71 71^ 


72 


AZIMUTHS 


/ 


o 


O ' O 


1 C 


o 





o 


|^0 


o 


o 


o 





o 


oo 


9O'O 


90*0 


90-0 


9<ro 


QO'O 


90-0 


90-0 


90'0 


90-0 


90*0 


90-0 


90-0 


9O'0 


90-0 


90'0 


01 


897 


897 


897 


89'7 


89-8 


89-8 


89-8 


89*8 


89-8 


89-8 


89-8 


89-8 


89-8 


89-8 


89-8 


02 


89-4 


89-5 


89-5 


89'5 


89-5 


89'5 


89-6 


89-6 


89-6 


89-6 


89-6 


89-6 


89-6 


89-6 


89-6 


03 


89-2 


89-2 


89-2 


89-2 


89-3 


89-3 


89-3 


89-4 


89-4 


89-4 


89-4 


89-4 


89-4 


89-5 


89-5 


04 


88'9 


88-9 


89-0 


89-0 


89-0 


89-1 


89-1 


8 9 -I 


89-2 


89-2 


89-2 


89-2 


89-3 


89-3 


89-3 


05 


88-6 


887 


887 


88-7 


88-8 


88-8 


88-9 


88'9 


89-0 


89-0 


89-0 


89-0 


8 9 -I 


89-1 


89-1 


06 


88-3 


88-4 


88-4 


88-5 


88-5 


88-6 


887 


887 


88-8 


88-8 


88-8 


88-9 


88-Q 


88-9 


88-9 


07 


88-1 


88-1 


88-2 


88-2 


88-3 


88-4 


88-4 


88-5 


88-6 


88-6 


88-6 


887 


88-7 


887 


88-8 


08 


87-8 


87-8 


87-9 


88-0 


88-1 


88-1 


88-2 


88-3 


88- 4 


88-4 


88-4 


88-5 


88-5 


88-5 


88-6 


09 


87-5 


87-6 


877 


87-7 


87-8 


87-9 


88-0 


88-1 


88-2 


88-2 


88-2 


88-3 


88-3 


88-4 


88-4 


10 


87-2 


87-3 


87-4 


87-5 


87-6 


877 


87-8 


87-9 


87'9 


88-0 


88-0 


88-1 


88-1 


88-2 


88-2 


II 


86-9 


87-0 


87-1 


87-2 


87-3 


87-4 


87-5 


87-6 


877 


87-8 


87-8 


87-9 


87-9 


88-0 


88-1 


12 


867 


86-8 


86-9 


87-0 


87-1 


87-2 


87'3 


87-4 


87-5 


87-6 


87-6 


877 


87-8 


87-8 


87-9 


13 


86-4 


86-5 


86-6 


86-7 


86-9 


87-0 


87-1 


87-2 


87-3 


87-4 


87-5 


87-5 


87-6 


87-6 


877 


14 


86-1 


86-2 


86-4 


86-5 


86-6 


867 


86-9 


87-0 


87-1 


87-2 


87-3 


87-3 


87H 


87'5 


87-5 


'IS 


85-8 


86-0 


86-1 


86-2 


86-4 


86-5 


86-6 


86-8 


86-9 


87-0 


87-1 


87-1 


87-2 


87'3 


87*3 


16 


85-6 


857 


85-8 


86-0 


86-1 


86-3 


86-4 


86-6 


867 


86-8 


86-9 


86-9 


87-0 


87-1 


87-2 


17 


85-3 


85-4 


85-6 


857 


85-9 


86-0 


86-2 


86-4 


86-5 


86-6 


867 


86-8 


86-8 


86-9 


87-0 


18 


85-0 


85-2 


85-3 


85'5 


85-6 


85-8 


86-0 


86-1 


86-3 


86-4 


86-5 


86-6 


86-6 


867 


86-8 


19 


847 


84-9 


85'i 


85-2 


85-4 


85-6 


85-8 


85-9 


86-1 


86-2 


86-3 


86-4 


86-5 


86-5 


86-6 


20 


84'5 


84-6 


84-8 


85-0 


85-2 


85-3 


85-5 


857 


85-9 


86-0 


86-1 


86-2 


86-3 


86-4 


86-5 


21 


84-2 


84M 


84-6 


84-7 


84-9 


85-1 


85-3 


85'5 


857 


85-8 


85-9 


86-0 


86-1 


86-2 


86-3 


'22 


83-9 


84-1 


84'3 


84-5 


84-7 


84-9 


85-1 


85'3 


85-5 


85-6 


857 


85-8 


85-9 


86-0 


86-1 


23 


83-6 


83-8 


84-0 


84-2 


84-4 


847 


84-9 


85-1 


85-3 


85-4 


85-5 


85-6 


857 


85-8 


85'9 


24 


83'4 


83-6 


83-8 


84-0 


84-2 


84-4 


84-6 


84-9 


85-1 


85-2 


85-3 


85'4 


85-5 


85-6 


85-8 


'25 


83'i 


8 3 '3 


83-5 


837 


84-0 


84-2 


84-4 


84-6 


84-9 


85-0 


85-1 


85-2 


85'3 


85'5 


85-6 


26 


82-8 


83-0 


83-3 


83-5 


837 


84-0 


84-2 


84-4 


847 


84-8 


84-9 


85-0 


85-2 


85-3 


85'4 


27 


82-5 


82-8 


83-0 


83-2 


83-5 


837 


84-0 


84-2 


84'5 


84-6 


847 


84-8 


85-0 


85-1 


85-2 


28 


82-3 


82-5 


82-8 


83-0 


83-3 


83-5 


83-8 


84-0 


84-3 


84-4 


84'5 


847 


84-8 


84-9 


8 5 -i 


29 


82-0 


82-2 


82-5 


82-8 


83-0 


83-3 


83-5 


83-8 


84-1 


84-2 


84-3 


84-5 


84-6 


847 


84-9 


"SO 


817 


82-0 


82-2 


82-5 


82-8 


83-0 


83-3 


83-6 


83'9 


84-0 


84-1 


84'3 


84-4 


84-6 


847 


'3 1 


81-5 


817 


82-0 


82-3 


82-5 


82-8 


83-1 


83H 


837 


83-8 


83-9 


84-1 


84-2 


84-4 


8 4 '5 


32 


81-2 


81-5 


817 


82-0 


82-3 


82-6 


82-9 


83-2 


83-5 


83-6 


83-8 


83'9 


84-1 


84-2 


84'4 


'33 


80-9 


81-2 


81-5 


81-8 


82-1 


82-4 


827 


83-0 


83-3 


83-4 


83-6 


837 


83-9 


84-0 


84-2 


*34 


80-6 


80-9 


81-2 


81-5 


81-8 


82-1 


82-4 


827 


83-1 


83-2 


83'4 


83'5 


837 


83-8 


84-0 


'35 


80-4 


807 


8ro 


81-3 


81-6 


81-9 


82-2 


82-5 


82-9 


83-0 


83-2 


8 3 '3 


83'5 


837 


83-8 


36 


80- 1 


80-4 


807 


81-0 


81-3 


817 


82-0 


82-3 


82-6 


82-8 


83-0 


83-1 


83-3 


83-5 


837 


'37 


79-8 


80- 1 


80-5 


80-8 


81-1 


81-4 


81-8 


82-1 


82-4 


82-6 


82-8 


83-0 


83-1 


83-3 


83-5 


38 


79-6 


79*9 


80-2 


80-5 


80-9 


81-2 


81-6 


81-9 


82-2 


82-4 


82-6 


82-8 


82-9 


83-1 


83'3 


'39 


79' 3 


79-6 


80-0 


80-3 


80-6 


8ro 


8i'3 


817 


82-0 


82-2 


82-4 


82-6 


82-8 


82-9 


83-1 


40 


79-0 


79' 4 


797 


80- 1 


80-4 


80-8 


81-1 


81-5 


81-8 


82-0 


82-2 


82-4 


82-6 


82-8 


83-0 


"4 1 


78-8 


79-1 


79'5 


79-8 


80-2 


80-5 


80-9 


81-3 


81-6 


81-8 


82-0 


82-2 


82-4 


82-6 


82-8 


42 


78-5 


78-8 


79'2 


79-6 


79*9 


80-3 


807 


81-1 


81-4 


81-6 


81-8 


82-0 


82-2 


82-4 


82-6 


'43 


78-2 


78-6 


79-0 


79-3 


797 


80- 1 


80-5 


80-8 


81-2 


81-4 


8r6 


81-8 


82-0 


82-2 


82-4 


"44 


78-0 


78-3 


787 


79-1 


79'5 


79-9 


80-2 


80-6 


81-0 


81-2 


81-4 


81-6 


81-8 


82-1 


82-3 


'45 


777 


78-1 


78'5 


78-8 


79-2 


79-6 


80-0 


80-4 


80-8 


8i'o 


81-3 


81-5 


817 


81-9 


82-1 


46 


77*4 


77-8 


78-2 


78-6 


79 -o 


79'4 


79-8 


80-2 


80-6 


80-8 


8ri 


81-3 


81-5 


817 


81-9 


'47 


77'2 


77-6 


78-0 


78-4 


78-8 


79*2 


79-6 


80-0 


80-4 


807 


80-9 


81-1 


81-3 


81-5 


817 


48 


76-9 


77'3 


777 


78-1 


78-5 


79-0 


79'4 


79-8 


80-2 


80-5 


807 


80-9 


81-1 


81-3 


8r6 


*49 


76-6 


77 -o 


77'5 


77'9 


78'3 


787 


79'2 


79*6 


80-0 


80-3 


80-5 


807 


80-9 


81-2 


81-4 


'50 


76-4 


76-8 


77'2 


77-6 


78-1 


78-5 


78-9 


79'4 


79-8 


80- 1 


80-3 


80-5 


80-8 


8i'o 


81-2 


5i 


76-1 


76-5 


77-0 


77'4 


77-8 


78-3 


787 


79-2 


79-6 


79'9 


80- 1 


80-3 


.80-6 


80-8 


81-0 


'52 


75'9 


76-3 


767 


77'2 


77-6 


78-1 


78-5 


79-0 


79*4 


797 


79'9 


80-2 


80-4 


80-6 


80-9 


"53 


75-6 


76*0 


76-5 


76-9 


77'4 


77'8 


78-,3 


78-8 


79'2 


79'5 


797 


80-0 


80-2 


80-5 


807 


'54 


75'3 


75-8 


76-2 


76-7 


77-1 


77'6 


78-1 


78-6 


79-0 


79'3 


79'5 


79'8 


80-0 


80-3 


80-5 



51 
Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 
Azimuth is named N or S according to the name of the A and B correction. 



AandB 
Cor- 
rection. 


LATITUDES. 


61 


62 


63 


64 


65 


66 


67 


68 


69 


69 


70 


70* 9 


71 


7ij 


72 


AZIMUTHS. 


i 

















o 


o 


o 


o 





o 


o 


o 


o 





'55 


75'i 


75'5 


76*0 


7 6- 4 


76-9 


77*4 


77-9 


78-4 


78-8 


79-1 


79'3 


79-6 


79-8 


80- 1 


8o- 4 


56 


74-8 


75'3 


75'7 


7 6-2 


76-7 


77*2 


77*7 


7 8'2 


787 


78-9 


79' 2 


79'4 


797 


79'9 


80-2 


57 


74-6 


75'o 


75'5 


76'O 


76-5 


76-9 


77*4 


77*9 


78-5 


787 


79*o 


79'2 


79'5 


797 


80*0 


58 


74*3 


74-8 


75'2 


75'7 


76-2 


76-7 


77'2 


77'7 


78-3 


78-5 


78-8 


79-0 


79*3 


79-6 


79*8 


'59 


74-0 


74'5 


75'0 


75'5 


76'O 


76-5 


77-0 


77*5 


7 8-I 


78-3 


78-6 


78-9 


79-1 


79'4 


797 


60 


73'8 


74'3 


74-8 


75*3 


75-8 


76-3 


76-8 


77*3 


77'9 


78-1 


78-4 


787 


78-9 


79*2 


79'5 


61 


73*5 


74-0 


74*5 


75'o 


75*5 


76-1 


76-6 


77-1 


77*7 


77*9 


78-2 


78-5 


78-8 


79*o 


79'3 


62 


73'3 


73'8 


74*3 


74'8 


75'3 


75*8 


76-4 


76-9 


77*5 


777 


78-0 


78-3 


78-6 


78-9 


79'2 


63 


73-0 


73'5 


74-0 


74-6 


75'i 


75-6 


76-2 


76-7 


77'3 


77-6 


77-8 


78-1 


78-4 


777 


79-0 


64 


72-8 


73'3 


73-8 


74'3 


74*9 


75*4 


76^0 


76-5 


77-1 


77'4 


777 


77.9 


78-2 


78-5 


78-8 


6 5 


72-5 


73*o 


73-6 


74-1 


74-6 


75-2 


75'7 


76-3 


76-9 


77'2 


77*5 


77-8 


78-1 


78-3 


78-6 


66 


72-3 


72-8 


73'3 


73'9 


74*4 


75'o 


75*5 


76-1 


767 


77-0 


77'3 


77'6 


77*9 


78-2 


78-5 


-67 


72-0 


72*5 


73'i 


73-6 


74*2 


74-8 


75'3 


75'9 


76-5 


76-8 


77-1 


77'4 


777 


78-0 


78-3 


68 


71-8 


72-3 


72-8 


73'4 


74-0 


74*5 


75*i 


75'7 


76-3 


76-6 


76-9 


77'2 


77'5 


77-8 


78-1 


69 


7i'5 


72-1 


72-6 


73'2 


737 


74'3 


74'9 


75'5 


76-1 


76-4 


767 


77-0 


77'3 


777 


78-0 


70 


7^3 


71-8 


72-4 


72-9 


73'5 


74-1 


74*7 


75*3 


75'9 


76-2 


76-5 


76-8 


77'2 


77*5 


77*8 


71 


71-0 


71-6 


72-1 


72'7 


73*3 


73*9 


74*5 


75-1 


75'7 


76*0 


76-4 


767 


77-0 


77*3 


77-6 


72 


70-8 


7!'3 


71-9 


72-5 


73'i 


73*7 


74'3 


74*9 


75'5 


75'8 


76-2 


76-5 


76-8 


77-1 


77'5 


'73 


7'5 


71-1 


71-7 


72-3 


72-9 


73'5 


74-1 


74*7 


75*3 


757 


76*0 


76-3 


76-6 


77-0 


77'3 


74 


70'3 


70-8 


71-4 


72-0 


72-6 


73'2 


73*9 


74*5 


75*i 


75'5 


75'8 


76-1 


76-5 


76-8 


77-1 


'75 


70-0 


70-6 


71-2 


71-8 


72-4 


73'0 


73'7 


74'3 


75-0 


75'3 


75'6 


75'9 


76-3 


76-6 


77*o 


76 


69-8 


70-4 


71-0 


71-6 


72-2 


72-8 


73*5 


74-1 


74-8 


75-1 


75'4 


75-8 


76'! 


76-4 


76-8 


'77 


69-5 


70-1 


70-7 


7!*3 


72-0 


72-6 


73'3 


73'9 


74-6 


74*9 


75'2 


75-6 


75'9 


76'3 


76-6 


78 


69-3 


69-9 


7'5 


71-1 


71-8 


72-4 


73'i 


73'7 


74'4 


747 


75*i 


75'4 


75'8 


76-1 


76-4 


'79 


69-0 


697 


7 P 3 


70-9 


7^5 


72-2 


72-8 


73*5 


74-2 


74'5 


74*9 


75'2 


75-6 


75'9 


76*3 


80 


68-8 


69-4 


70*0 


70-7 


?i'3 


72-0 


72*6 


73*3 


74-0 


74*3 


747 


75'0 


75'4 


75-8 


76-1 


81 


68-6 


69-2 


69-8 


7'5 


71-1 


71-8 


72-4 


73*i 


73-8 


74*2 


74'5 


74*9 


75*2 


75-6 


75'9 


82 


68-^ 


68-9 


69-6 


70-2 


70-9 


71-6 


72-2 


72-9 


73-6 


74*o 


74*3 


747 


75'i 


75*4 


75-8 


83 


68-1 


68-7 


69-4 


70-0 


70-7 


71*3 


72*0 


72-7 


73'4 


73-8 


74*2 


74*5 


74*9 


75'2 


75-6 


84 


67-8 


68-5 


69-1 


69-8 


7<>-5 


71-1 


71-8 


72'5 


73*2 


73'6 


74-0 


74*3 


747 


75'i 


75'4 


85 


67-6 


68-2 


68-9 


69-6 


70-2 


70-9 


71*6 


72-3 


73'i 


73'4 


73-8 


74-2 


74*5 


74'9 


75'3 


86 


67-4 


68-0 


68-7 


69-3 


7O'o 


70-7 


71-4 


72-1 


72-9 


73'2 


73'6 


74-0 


74'4 


747 


75'i 


87 


67-1 


67-8 


68-4 


69-1 


69-8 


70-5 


71-2 


71-9 


727 


73*i 


73*4 


73-8 


74*2 


74-6 


75-o 


88 


66-9 


67-6 


68-2 


68-9 


69-6 


70*3 


71-0 


71-8 


72-5 


72-9 


73'2 


73-6 


74-0 


74*4 


74-8 


89 


66-7 


67-3 


68-0 


68-7 


69-4 


70-1 


70'8 


7i'6 


72-3 


727 


73'i 


73'5 


73'8 


74' 2 


74-6 


90 


66-4 


67-1 


67-8 


68-5 


69-2 


69-9 


70-6 


71-4 


72-1 


72*5 


72-9 


73'3 


737 


74-1 


74*5 


91 


66-2 


66-9 


67-6 


68-3 


69-0 


69-7 


70-4 


71-2 


71-9 


72-3 


727 


73'i 


73'5 


73'9 


74'3 


92 


66-0 


66-6 


67-3 


68-0 


68-8 


69-5 


70-2 


71-0 


71-8 


72-1 


72'5 


72-9 


73'3 


737 


74-1 


'93 


65*7 


66-4 


67-1 


67-8 


68-5 


69-3 


70*0 


70-8 


71-6 


72-0 


72'4 


72-8 


73*2 


73-6 


74-0 


'94 


65-5 


66-2 


66-9 


67-6 


68-3 


69-1 


69-8 


7O'6 


71-4 


71-8 


72-2 


72-6 


73*o 


73'4 


73*8 


'95 


OS'S 


66-0 


66-7 


67H 


68-1 


68-9 


69-6 


70-4 


71-2 


71-6 


72-0 


72-4 


72-8 


73'2 


73'6 


96 


65-0 


65-7 


66-5 


67-2 


67-9 


68-7 


69-4 


70-2 


71-0 


71-4 


71-8 


72-2 


72*6 


73'i 


73'5 


'97 


64-8 


65'5 


66-2 


67-0 


67-7 


68-5 


69-2 


7O'O 


70-8 


71-2 


71-6 


72-1 


72-5 


72-9 


73*3 


98 


64-6 


65-3 


66-0 


66-8 


67-5 


68-3 


69-0 


69-8 


70-6 


71-1 


7i*5 


71-9 


72'3 


727 


73'2 


'99 


64-4 


65-1 


65-8 


66-5 


67-3 


68-1 


68-9 


697 


7*5 


70-9 


71-3 


717 


72-1 


72-6 


73'o 


oo 


64-1 


64-9 


65-6 


66-3 


67-1 


67-9 


68-7 


69'5 


7<>*3 


707 


71-1 


7 1 '5 


72-0 


72-4 


72-8 


02 


63'7 


64-4 


65-2 


65-9 


66-7 


67-5 


68-3 


69-1 


69-9 


7<>*3 


70-8 


71-2 


71-6 


72-1 


72-5 


04 


63-2 


64-0 


64-7 


65-5 


66-3 


67-1 


67-9 


687 


69-6 


70-0 


70-4 


70-9 


7 J '3 


717 


72-2 


06 


62-8 


63'5 


64*3 


65-1 


65'9 


66-7 


67-5 


68-3 


69-2 


69-6 


70-1 


7'5 


71-0 


71-4 


71-9 


08 


62-4 


63-1 


63-9 


64-7 


65*5 


66-3 


67-1 


68-0 


68-8 


69-3 


697 


70-2 


70-6 


7 1 '* 


7i'5 


10 


61-9 


62-7 


63'5 


64-3 


65-1 


65'9 


66-7 


67-6 


68-5 


68-9 


69-4 


69-8 


70*3 


70-8 


71-2 


12 


61-5 


62-3 


63-0 


63-9 


64-7 


65-5 


66-4 


67-2 


68-1 


68-6 


69-0 


69-5 


70*0 


70-4 


70-9 


14 


61-1 


61-8 


62-6 


63-4 


64-3 


65-1 


66-0 


66-9 


67-8 


68-2 


687 


69-2 


69-6 


70-1 


70-6 


16 


60-6 


61-4 


62-2 


63*0 


63-9 


64-7 


65-6 


66-5 


67-4 


67-9 


68-4 


68-8 


69'3 


69-8 


70'3 


18 


60-2 


61*0 


61-8 


62-6 


63-5 


64-4 


65-2 


66-2 


67-1 


67'5 


68-0 


68-5 69-0 


69*5 


70*0 



52 
Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 
Azimuth is named N or S according to the name of the A and B correction. 



AandB 
Cor- 
rection. 


LATITUDKS. 


61 


82 


83 


i 
64 


85 


88 


67 


68 3 


69 


69* 


70 


70i 


71 


71* 


IV 




AZIMUTHS. 


2O 


59'8 


60-6 


61-4 


62-3 


6 3 -l 


64-0 


64-9 


65-8 


66-7 


6 7 -2 


677 


68-2 


687 


6 9 -2 


697 


22 


59'4 


60'2 


6i'o 


61-9 


627 


63-6 


64-5 


65'4 


66-4 


66-9 


67-4 


67-8 


68-3 


68-8 


69-3 


24 


59*o 


59'8 


60-6 


61-5 


62- 3 


63-2 


64-1 


6 5 -I 


66-0 


66-5 


67^0 


67-5 


68-0 


68-5 


69*0 


26 


58-6 


59'4 


60-2 


61-1 


62'0 


62-9 


63-8 


647 


657 


66-2 


667 


67-2 


677 


68-2 


687 


28 


58-2 


59*o 


59'8 


607 


61-6 


62-5 


63H 


64H 


65-4 


65-9 


66-4 


66-9 


67-4 


67-9 


68-4 


30 


57-8 


58-6 


59'5 


60*3 


61-2 


62-1 


6 3 -l 


64^0 


65-0 


65-5 


66-0 


66-5 


67-1 


67-6 


68-1 


32 


57'4 


58-2 


59'i 


59'9 


60-8 


61-8 


62*7 


637 


647 


65-2 


657 


66-2 


667 


67*3 


67-8 


'34 


57'o 


57-8 


587 


59'6 


60-5 


61-4 


62-4 


6 3 -3 


64-3 


64-9 


6 5 '4 


65'9 


66-4 


67-0 


67-5 


36 


56-6 


57*4 


58-3 


59'2 


60- 1 


61-1 


62-0 


63-0 


64-0 


64-5 


65-1 


65-6 


66-1 


667 


67-2 


38 


56-2 


57 'i 


57'9 


58-8 


597 


607 


617 


627 


637 


64-2 


647 


65-3 


65-8 


66-4 


66-9 


40 


55'8 


56-7 


57-6 


58-5 


59'4 


60-3 


61-3 


62-3 


63H 


63-9 


64-4 


65-0 


65-5 


66-0 


66-6 


42 


55'5 


56'3 


57*2 


58-1 


59'0 


6o'o 


6i'O 


62-0 


63-0 


63-6 


64-1 


64-6 


65-2 


657 


66-3 


"44 


55'i 


55'9 


56-8 


577 


587 


59'6 


60-6 


61-7 


627 


63-2 


63-8 


64-3 


64-9 


65-4 


66-0 


46 


54'7 


55-6 


56-5 


57'4 


58'3 


59'3 


60-3 


61-3 


62-4 


62-9 


63-5 


64-0 


64-6 


65-1 


657 


48 


54'3 


55'2 


56-1 


57'o 


58-0 


59'0 


6o'o 


61*0 


62-1 


62-6 


63-2 


637 


64-3 


64-8 


65-4 


50 


54*o 


54-8 


55'7 


567 


57-6 


58-6 


59'6 


60-7 


617 


62-3 


62-8 


63-4 


64^0 


64-5 


65-1 


52 


53-6 


54*5 


55'4 


56'3 


57'3 


58-3 


59'3 


60-3 


61-4 


62'O 


62-5 


63-1 


637 


64-3 


64-8 


'54 


53*3 


54' i 


55'Q 


56-0 


56-9 


57'9 


59'0 


6o'o 


61-1 


61-7 


62-2 


62-8 


63-4 


64*0 


64-6 


56 


52-9 


53'8 


547 


55-6 


56-6 


57'6 


58-6 


597 


60-8 


61-4 


61-9 


62-5 


6 3 'i 


637 


64-3 


58 


52'5 


53*4 


54*3 


55*3 


56-3 


57*3 


58-3 


59'4 


60-5 


6i'o 


61-6 


62-2 


62-8 


63*4 


64-0 


60 


52-2 


53'i 


54* 


55*o 


55'9 


56-9 


58-0 


59'i 


60-2 


60* 7 


61-3 


6i'9 


62-5 


63-1 


637 


62 


5i*9 


527 


537 


54-6 


55-6 


56-6 


577 


587 


59'9 


60*4 


6ro 


61-6 


62-2 


62-8 


63-4 


64 


5i'5 


52-4 


53'3 


54'3 


55'3 


56-3 


57*3 


58-4 


59*6 


60- 1 


607 


61-3 


61-9 


62-5 


63-1 


66 


51-2 


52-1 


53'o 


54*0 


54'9 


56-0 


57' 


58-1 


59'3 


59'8 


60-4 


6i'o 


61-6 


62-2 


62-8 


68 


50-8 


Si'? 


527 


53'6 


54'6 


557 


567 


57-8 


58-9 


59'5 


60- 1 


607 


61-3 


61-9 


62-6 


70 


50'5 


5i'4 


52*3 


53*3 


54'3 


55'3 


56-4 


57'5 


58-6 


59'2 


59'8 


60-4 


6i'o 


617 


62-3 


72 


50-2 


5i'i 


52-0 


53'o 


54' 


55'0 


56-1 


57*2 


58-4 


58-9 


59'5 


60- 1 


60-8 


61-4 


62'O 


74 


49*9 


50-8 


517 


527 


537 


547 


55'8 


56-9 


58-1 


58-6 


59*2 


59'9 


60-5 


61-1 


617 


76 


49*5 


50'4 


5i*4 


52-3 


53'4 


54*4 


55*5 


56-6 


57'8 


58-4 


59'0 


59'6 


60-2 


60-8 


61-5 


78 


49'2 


50-1 


51*1 


52-0 


53'o 


54'i 


55'2 


56-3 


57'5 


58-1 


587 


59'3 


59'9 


60-5 


61-2 


80 


48-9 


49-8 


507 


517 


527 


53-8 


54*9 


56*0 


57'2 


57-8 


58-4 


59'0 


59'6 


60-3 


60-9 


82 


48-6 


49' 5 


50-4 


5i'4 


52-4 


53'5 


54-6 


557 


56-9 


57*5 


58-1 


587 


59*4 


60*0 


60-6 


84 


48-3 


49*2 


50-1 


5i*i 


52-1 


53'2 


54*3 


55'4 


56-6 


57*2 


57-8 


58-4 


59*i 


597 


60-4 


86 


48-0 


48-9 


49'8 


50-8 


51-8 


52*9 


54' 


55'i 


56-3 


56-9 


57*5 


58-2 


58-8 


59*5 


60- 1 


88 


477 


48-6 


49'5 


50'5 


5i*5 


52-6 


537 


54-8 


56-0 


56-6 


57'3 


57'9 


58-5 


59*2 


59'8 


90 


47*4 


48-3 


49-2 


50*2 


5i'2 


52-3 


53*4 


54'6 


557 


56-4 


57*o 


57-6 


58-3 


58-9 


59-6 


92 


47-1 


48-0 


48-9 


49'9 


50-9 


52-0 


53*i 


54'3 


55*5 


56-1 


567 


57'3 


58-0 


58-6 


59*3 


"94 


46-8 


47*7 


48-6 


49-6 


50-7 


5i7 


52-8 


54'o 


55*2 


55-8 


56-4 


57'i 


577 


58-4 


59'i 


96 


4 6 '5 


47'4 


48-3 


49'3 


50H 


5i'4 


52-6 


537 


54'9 


55'5 


56-2 


56-8 


57'5 


58-1 


58-8 


98 


46-2 


47-1 


48-0 


49-0 


50-1 


51-2 


52'3 


53'4 


54-6 


55*3 


55'9 


56-5 


57'2 


57 '9 


58-5 


2*00 


45'9 


46-8 


47 -8 


48-8 


49*8 


50*9 


52-0 


53'2 


54*4 


55'o 


55'6 


56-3 


56-9 


57'6 


58-3 


2-05 


45'2 


46-1 


47-1 


4 8-i 


49-1 


50-2 


5i'3 


52-5 


537 


54'3 


55*0 


55-6 


56-3 


57*0 


57'6 


2'IO 


44'5 


45'4 


46-4 


47'4 


48-4 


49'5 


50-6 


51-8 


53'0 


537 


54*3 


55 4 o 


55-6 


56-3 


57'0 


2-15 


43'8 


447 


457 


467 


477 


48-8 


50-0 


5i'2 


52-4 


53*0 


537 


54*3 


55*0 


557 


56-4 


2*2O 


43*2 


44-1 


45'0 


46-0 


47-1 


48-2 


49' 3 


50-5 


517 


52'4 


53'0 


537 


54*4 


55'i 


55-8 


2'2 5 


42*5 


43'4 


44'4 


45'4 


46-4 


47*5 


487 


49'9 


SIT 


51-8 


52*4 


53'i 


53-8 


54*5 


55'2 


2-30 


41-9 


42-8 


43-8 


44-8 


45-8 


46-9 


48-1 


49'3 


50'5 


5i'i 


5i-8 


52'5 


53*2 


53'9 


54'6 


2-40 


40-7 


41-6 


42-5 


43'5 


44-6 


457 


46-8 


48-0 


49'3 


50-0 


5 '6 


5i'3 


52-0 


527 


53*4 


2-50 


39*5 


40-4 


41-4 


42-4 


43'4 


44*5 


457 


46-9 


48-1 


48-8 


49'5 


50-2 


50*9 


51-6 


52-3 


2'6o 


38-4 


39'3 


40'3 


4i'3 


42'3 


43*4 


44'5 


45-8 


47-0 


477 


48-4 


49'0 


49-8 


50-5 


5i'2 


2-70 


37*4 


38-3 


39-2 


40-2 


41-2 


4 2 '3 


43*5 


447 


45'9 


46-6 


47'3 


48-0 


487 


49'4 


50-2 


2-80 


36-4 


37'3 


38-2 


39-2 


40-2 


4i'3 


42-4 


43-6 


44'9 


45'6 


46-2 


46-9 


47-6 


48-4 


49-1 


2-90 


35*4 


36-3 


37-2 


38-2 


39-2 


40-3 


41-4 


42-6 


43'9 


44-6 


45*2 


45'9 


46-6 


47*4 


48-1 


3-00 


34*5 


35'4 


36-3 


37'2 


38-3 


39*3 


4*5 


41-7 


42-9 


43-6 


44'3 


45*o 


457 


46-4 


47*2 


3-10 


33'6 


34'5 


35'4 


36-3 


37'4 


38-4 


39'5 


407 


42-0 


42-6 


43'3 


44-0 


447 


45'5 


46-2 



53 
Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 

Azimuth is named N or S according to the name of the A and B correction. 



AandB 
Cor- 
rection. 


LATITUDES. 


61 


62 


63 


64 


65 1 66 


67 68 


69 


69i 


70 


w 


71 


Hi- 


72 


AZIMUTHS. 


i 





o 


o 


| 


o o o 





O 





O | O 


o 


o 


3'20 


3 2-8 


33-6 


34'5 


35-5 36-5 


37'5 


387 


39*8 


4I'1 


417 


42-4 


43-1 


43-8 


44-6 


45'3 


3'3 


32-0 


32-8 


337 


347 


35-6 


367 


37*8 39*0 


40-2 


40-9 


41-5 


4 2-2 


42-9 


437 


44*4 


3*40 




32-1 


32'9 


33*9 


34-8 


35'9 


37' 


38-1 


39'4 


40-0 


407 


41-4 


42-1 


42-8 


43*6 


3-60 


29-8 


30-6 


3 X '5 


32-4 


33'3 


34'3 


35'4 


36-6 


37-8 


38-4 


39' I 


39*8 


40-5 


41-2 


42-0 


3'8o 


28-5 


29-3 


30-1 


31-0 






34' 


35'i 


36-3 


36-9 


37-6 


38-3 




397 


40-4 


4-00 


2 7'3 


28-0 


28*8 


297 


30-6 


31-6 


32'6 


337 


34*9 


35-5 


36-2 


36-8 


37'5 


38-2 


39-0 


4-20 


26'2 


26-9 


277 


28-5 


2 9'4 


30-3 


31*4 


32-4 


33-6 


34*2 


34'8 


35'5 


36-2 


36-9 


37-6 


4-40 


25*1 


25-8 


26*6 


27*4 


28-3 


29-2 


30-2 


31-2 


32-4 




33-6 


34*2 


34*9 


35'6 


36-3 


4-60 


24-2 


24-8 


25-6 


26-4 


27-2 


28-1 


29-1 


30-1 


31-2 


31*8 


32'4 


33*i 


337 


34'4 


35'i 


4-80 




23*9 


24-6 


25*4 


26-2 


27-1 


28-1 


29-1 


30-2 


307 


3 J '3 


32-0 


32-6 


33'3 


34' 


5-00 


22'4 


23-1 


23-8 


24-5 


25-3 


26-2 


27-1 


28-1 


29-2 


297 


30-3 


30-9 


31-6 


32'2 


32*9 


5-20 


21-6 


22-3 


23-0 


237 


24-5 


25*3 


26-2 


27-2 


28-2 


28-8 


29-3 


29-9 


30*6 


31-2 


31*9 


5*4 


20-9 


21-5 


22'2 


22-9 


237 




25-4 


26-3 


2 7'3 


27*9 


28-4 


29*0 


29-6 


30-3 


30-9 


5'6o 


2O'2 


20-8 


21-5 


22-2 


22-9 


237 


24-6 


2 5'5 


26-5 


27-0 


27-6 


28-1 


287 


29-4 


30-0 


5-80 


19*6 


2O'2 


20-8 


21-5 


22 - 2 


23*0 


23-8 


247 


257 


26-2 


26-8 


27-3 


27-9 


28-5 


29-2 


6'oo 


I9'O 


19*5 


20'2 


20-8 


21-5 


22-3 


23-1 


24-0 


24-9 


25M 


26*0 


26-5 


27-1 


277 


28-3 


6'2O 


i8'4 


19*0 


I9'6 


20*2 


20'9 


21'6 


22-4 




24-2 


247 


25-2 


25-8 


26-4 


26*9 


27*6 


6*40 


17-9 


18-4 


ig-0 


19-6 


20'3 


21'0 


21-8 


22-6 


23-6 


24-0 


24-6 


25-1 


25-6 


26-2 


26-8 


6-60 


17-4 


17*9 


18-5 


19-1 


197 


20'4 


21'2 


22'O 


22-9 


23'4 


23-9 


24-4 


25-0 


25*5 


26*1 


6-80 




17-4 


17-9 


18-5 


19-2 


19-9 


20'6 


21'4 


22'3 


22-8 


23'3 


23-8 


24'3 


24-9 


25*4 


7'oo 


16-4 


16*9 


i7'5 


18-0 


187 


19-4 


2O* I 


20'9 


217 


22'2 


227 


23*2 


237 


24-2 


24-8 


7-20 


i6'O 


16-5 


17-0 


17-6 


18-2 




19-6 


20-3 


21'2 


21-6 


22'I 


22-6 


23-1 


23*6 


24-2 


7-40 


15*6 


16-1 


16-6 


17-1 


177 


18*4 


19*1 


I9-8 


207 


2I'J 


21-6 


22'0 


22-5 


23-1 


23*6 


7-60 


I5' 2 


157 


16-2 


167 


17-3 


17-9 


18-6 


I9-4 


2O'2 


2O'6 


2I*O 


21'5 


22*0 


22-5 


23-1 


7'8o 


14-8 


I5-3 


15-8 


16-3 




i7'5 


18-2 


18-9 


197 


2O'I 


20-5 


21'0 


21'5 


22'0 


22-5 


8'oo 


J 4'5 


14-9 


J 5'4 


I5'9 


16-5 


17-1 


17-7 


18-5 


I9-2 


19-6 


2O'I 


20-5 


2I'O 


21-5 


22'0 


8'20 


14*1 


14-6 


15-0 




16-1 


167 


i7'3 


18-0 


18-8 


19-2 


I9'6 


2O'I 


20-5 


21'0 


21'5 


8-40 


13-8 


1.4-2 


147 


15-2 


157 


16-3 




17-6 


18-4 


18-8 


I9-2 


I9'6 


2O'I 


2O'6 


2I'I 


8-60 


J 3'5 




14-4 


14-9 




16*0 


16-6 


17-2 


18-0 


18-4 


18-8 


19-2 


197 


20*1 


20-6 


8-80 


13-2 


13-6 


14-1 


14-5 


1 5' 1 


15-6 1 16-2 


16-9 


17-6 


18-0 


18-4 


18-8 


19-2 


X97 


20'2 


9-00 
9*20 


12-9 
12-6 


13*3 
13-0 


i 3 ;8 


14-2 


147 
14-4 


15*3 
15-0 


15-9 
I5-5 


16-5 
16-2 


17-2 
16-9 


17-6 
17-2 


18-0 
17-6 


X8' 4 

18-0 


18-8 
18-5 


I9-3 
18-9 


19-8 
I9- 4 


9-40 

9'6o 


12-4 


12*8 

12-5 


13-2 

12 9 


13-6 


14*1 


147 
14-4 


14-9 


15*9 
I5-5 


16-5 
16-2 


16-9 
16-6 


ll'-l 


177 
17*3 


18-1 
177 


18-5 
18-2 


18-6 


9-80 


ii'9 


12-3 


127 


13*1 13-6 


14-1 


14*6 


15-2 


I5-9 


16-2 


16-6 


17*0 


17-4 


17-8 


18-3 


IO'O 


117 


I2'0 


12-4 


12-9 


J 3'3 


13-8 


14-4 


14-9 


15-6 


15-9 


16-3 


167 


17-1 


J 7'5 


17-9 


II'O 


io'6 


II'O 


11-3 


117 


12*1 


I2'6 




13-6 


14-2 


14-6 


14-9 


15-2 


15-6 


16*0 


16*4 


I2'0 


g-8 


lO'I 


10*4 


10-8 


11*2 


11 '6 


I2'O 


12-5 


13-1 


13*4 


137 


14-0 


14-4 


147 


I 5' 1 


13-0 


9*0 


9'3 


9-6 


IO % O 


I0'3 


107 


II'I 


n-6 




12*4 


127 


13-0 


I3-3 


13*6 


14-0 


I 4 '0 


8'4 


87 


8-9 


9'3 


9*6 


IO'O 


IO- 4 


10-8 


ii'3 


"5 


ii-8 


12*1 


12-4 


127 


13-0 


16*0 


7"3 


7-6 


7'8 


8-1 


8-4 


87 


9-1 


9'5 


9'9 


lO'I 


10-4 


10-6 


10-9 


ii'i 


ii'4 


18-0 




67 


7-0 


7-2 


7*5 


7-8 


8-1 


8-4 


8-8 


g-o 


9-2 


9'4 


97 


9'9 


IO'2 


2O'O 


5'9 






6-5 


67 


7-0 


7*3 


7-6 


7*9 


8-1 


8'3 


8*5 


87 


9-0 


9' 2 


22-0 
24-0 


5'4 
4-9 


5'5 


57 


5'9 
5'4 


6-1 
5-6 


6-4 


6-6 
6-1 


6-9 
6-3 


7-2 
6-6 


7*4 
67 


7-6 
6-9 


7-1 


7-9 
7*3 


8'2 

7*5 


8-4 

77 


26'O 
28-0 


4'5 
4-2 


47 
4'4 


4-8 
4*5 


5-0 
47 


V8 


5'4 


5*2 


5'9 
5'4 


6-i 

57 


6-3 


6-4 
6-0 


6-6 
6-1 


67 
6'3 


6-9 
6-4 
fvn 


7-1 
6-6 

6'2 


3O*O 


3'9 


4' 1 


4-2 


4'3 


4*5 


47 


4*9 


5' 1 


5'3 


5*4 


5*6 


57 


5 a 


O w 


. .p. 


40-0 

50*0 


3-0 


3-0 

2' 4 




3'3 
2-6 


3'4 
27 


3'5 

2'8 


37 
2-9 


3-i 


4-0 


3'3 


3'3 


4'3 
3*4 


4'4 
3*5 


4*5 
3-6 


4 
37 


70-0 

lOO'O 


17 

1*2 


17 

1*2 


1-8 
1*3 


1-9 


1-9 

1-4 


2'O 

1*4 


i'5 


2'2 


2'3 
1-6 


2-3 
1-6 


2'4 

17 


17 


1-8 


2-6 
1-8 


2-6 

1-9 


200'O 


0-6 


0-6 


0-6 


07 


07 


07 


07 


0*8 


0-8 


0-8 


0-8 


0-9 


0-9 


0-9 


0-9 


4OO'0 
8OO*0 


0-3 

O'l 


0-3 
0*2 


0'2 


0-3 

0'2 


0-3 

0'2 


0-4 

0*2 


0-4 

O'2 


0-4 

O'2 


0-4 

O'2 


0-4 

O"2 


0*4 

0'2 


0-4 

0'2 


"4 

0'2 


O'2 


0'2 



54 
Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 

Azimuth is named N or S according to the name of the A and B correction. 



AandB 
Cor- 
rection. 


LATITUDES. 


73 


Itf 


75 


76 


77 


78 


79 


80 


81 82 


83 


m 


84 ! 84$ 


85 


AZIMUTHS. 


i 


o 


o 


o 


o 


o 


O . I O 1 O O 








o 





o 


oo 


9O'O 


90-0 


90*0 


9O'o 


90'0 


90-0 


90-0 


90'O 


90-0 


90-0 


90-0 


go-o 


90-0 


90-0 


90'0 


02 


897 


897 


897 


897 


897 


89-8 


89-8 


89-8 


89-8 


89-8 


89-9 


89-9 


89-9 


89-9 


89-9 


04 


89-3 


89-4 


89-4 


89-4 


89-5 


89-5 


89-6 


89-6 


89-6 


897 


897 


897 


89-8 


89-8 


89-8 


06 


89-0 


89-1 


89-1 


89-2 


89-2 


89-3 


89-3 


89-4 


89-5 


89-5 


89-6 


89-6 


89-6 


897 


897 


08 


887 


887 


88-8 


88-9 


89-0 


89-0 


8 9 -I 


89-2 


89*3 


89-4 


89H 


89-5 


89-5 


89-6 


89-6 


10 


88-3 


88-4 


88-5 


88-6 


88-7 


88-8 


88-9 


89-0 


89-1 


89-2 


89-3 


89-4 


89-4 


89-5 


89-5 


'12 


88-0 


88-1 


88-2 


88-3 


88-5 


88-6 


88-7 


88-8 


88-9 


89-0 


89-2 


89-2 


89-3 


89-3 


89-4 


14 


877 


87-8 


87-9 


88-1 


88-2 


88-3 


88- s 


88-6 


88-7 


88-9 


89-0 


89-1 


89-2 


89-2 


89-3 


16 


87-3 


87-5 


87-6 


87-8 


87-9 


88-1 


88-3 


88-4 


88-6 


88-7 


88-9 


89-0 


89-0 


89-1 


89-2 


18 


87-0 


87-2 


87-3 


87*5 


87-7 


87-9 


88-0 


88-2 


88-4 


88-6 


887 


88-8 


88-9 


89-0 


8 9 -I 


20 


867 


86-8 


87-0 


87-2 


87H 


87-6 


87-8 


88-0 


88-2 


88-4 


88-6 


88-7 


88-8 


88-9 


89-0 


22 


86-3 


86-5 


86-7 


87-0 


87-2 


87-4 


87-6 


87-8 


88-0 


88-2 


88-5 


88-6 


887 


88-8 


88-9 


24 


86-0 


86-2 


86-4 


86-7 


86-9 


87-1 


87-4 


.87-6 


87-8 


88-x 


88-3 


88-4 


88-6 


887 


88-8 


26 


85-7 


85-9 


86-2 


86-4 


86-7 


86-9 


87-2 


87-4 


877 


87-9 


88-2 


88-3 


88-4 


88-6 


88-7 


28 


85-3 


85-6 


859 


86-1 


86-4 


867 


86-9 


87-2 


87-5 


87-8 


88-0 


88-2 


88-3 


88-5 


88-6 


30 


85-0 


85-3 


85-6 


85-8 


86-1 


86-4 


86-7 


87-0 


87-3 


87-6 


87-9 


88-1 


88-2 


88-4 


88-5 


3 2 


847 


85-0 


85-3 


85-6 


85-9 


86-2 


86-5 


86-8 


87-1 


87-4 


87-8 


87-9 


88-1 


88-2 


88-4 


'34 


84-3 


84-6 


85-0 


85-3 


85-6 


86-0 


86-3 


86-6 


87-0 


87*3 


87-6 


87-8 


88-0 


88-1 


88-3 


36 


84-0 


84-3 


847 


85-0 


85-4 


857 


86-1 


86-4 


86-8 


87-1 


87-5 


87-7 


87-8 


88-0 


88-2 


38 


837 


84-0 


84-4 


847 


85-1 


85-5 


85-9 


86-2 


86-6 


87-0 


87-3 


87-5 


87-7 


87-9 


88-1 


40 


83'3 


837 


84-1 


84-5 


84-9 


85-2 


85-6 


86-0 


86-4 


86-8 


87-2 


87-4 


87-6 


87-8 


88-0 


42 


83-0 


83'4 


83-8 


84-2 


84-6 


85-0 


8 5 '4 


85-8 


86-2 


86-7 


87-1 


87-3 


87-5 


877 


87-9 


"44 


82-7 


83-1 


83-5 


83*9 


84-3 


84-8 


85-2 


85-6 


86-1 


86-5 


86-9 


87-1 


87H 


87-6 


87-8 


46 


8^3 


82-8 


83-2 


837 


84-1 


84-5 


85-0 


85-4 


85-9 


86-3 


36-8 


87-0 


87-2 


87-5 


87-7 


48 


82'O 


82-5 


82-9 


83*4 


83-8 


84-3 


84-8 


85-2 


857 


86-2 


86-7 


86-9 


87-1 


87-4 


87-6 


50 


81-7 


82-2 


82-6 


83-1 


83-6 


84-1 


84-6 


85-0 


85-5 


86-0 


86-5 


86-8 


87-0 


87'3 


87'5 


52 


81-4 


8r8 


82-3 


82-8 


83-3 


83-8 


84-3 


84-8 


85-3 


85-9 


86-4 


86-6 


86-9 


87-1 


87-4 


*54 


8ro 


81-5 


82-0 


82-6 


83-1 


83-6 


84-1 


84-6 


85-2 


857 


86-2 


86-5 


86-8 


87-0 


87-3 


56 


80-7 


81-2 


8r8 


82-3 


82-8 


83-4 


83-9 


84-4 


85-0 


8 5 -5 


86-1 


86-4 


86-6 


86-9 


87-2 


58 


80-4 


80-9 


8r 5 


82-0 


82-6 


83-1 


837 


84-2 


84-8 


85-4 


86-0 


86-2 


86-5 


86-8 


87-1 


60 


80- 1 


80-6 


81-2 


81-7 


82-3 


82-9 


83-5 


84-1 


84-6 


85-2 


85-8 


86-1 


86-4 


86-7 


87-0 


62 


797 


80-3 


80-9 


8i'5 


82-1 


82-7 


83-3 


83-9 


84-5 


85-1 


857 


86-0 


86-3 


86-6 


86-9 


64 


79*4 


80-0 


80-6 


81-2 


8r8 


82-4 


83-0 


837 


84-3 


84-9 


85-5 


85-9 


86-2 


86-5 


86-8 


66 


79-1 


797 


80-3 


80-9 


81-6 


8-J-2 


82-8 


83-5 


84-1 


84-8 


85-4 


857 


86-1 


86-4 


86-7 


68 


78-8 


79'4 


80-0 


80-7 


81-3 


82'O 


82-6 


833 


83-9 


84-6 


85-3 


85-6 


85-9 


86-3 


86-6 


70 


78-4 


79-1 


797 


80-4 


81-1 


817 


82-4 


83-1 


83-8 


84-4 


85-1 


85-5 


85-8 


86-2 


86-5 


72 


78-1 


78-8 


79'4 


80- 1 


80-8 


8r 5 


82-2 


82-9 


83-6 


84-3 


85-0 


85-3 


857 


86-1 


86-4 


'74 


77-8 


78-5 


79-2 


79'9 


80-5 


81-3 


82-0 


82-7 


83H 


84-1 


84-8 


85-2 


85-6 


85*9 


86-3 


76 


77'5 


78-2 


78-9 


79-6 


80-3 


8ro 


8r 7 


82-5 


83-2 


84-0 


847 


85-1 


85-5 


85-8 


86-2 


78 


77-2 


77'9 


78-6 


79-3 


80-0 


80-8 


8i'5 


82-3 


83-0 


83-8 


84-6 


85-0 


85-3 


857 


86-1 


80 


76-8 


77-6 


78-3 


79*o 


79-8 


80-6 


81-3 


82-1 


82-9 


83-6 


84-4 


84-8 


85-2 


85-6 


86-0 


82 


76-5 


77*3 


78-0 


78-8 


79'5 


80-3 


81-1 


81-9 


827 


83-5 


84-3 


847 


85-1 


85-5 


85-9 


84 


76-2 


77-0 


777 


78-5 


79'3 


80- 1 


80-9 


81-7 


82-5 


83-3 


84-2 


84-6 


85-0 


85-4 


85-8 


86 


75*9 


76-7 


77*5 


78-2 


79-1 


79-9 


80-7 


8i'5 


82-3 


83-2 


84-0 


84-4 


84-9 


85-3 


857 


88 


75-6 


76-4 


77'2 


78-0 


78-8 


79-6 


80-5 


81-3 


82-2 


83-0 


83-9 


84-3 


847 


85-2 


85-6 


90 


75'3 


76-1 


76-9 


777 


78-6 


79'4 


80-3 


8ri 


82-0 


82-9 


837 


84-2 


84-6 


85-1 


85-5 


92 


74'9 


75-8 


76-6 


77'5 


78-3 


79'2 


80-0 


80-9 


81-8 


827 


83-6 


84-1 


84-5 


85-0 


85H 


'94 


74-6 


75'5 


76-3 


77-2 


78-1 


78-9 


79-8 


80-7 


81-6 


82-5 


83'5 


83-9 


84H 


84-9 


85-3 


96 


74'3 


75*2 


76-0 


76-9 


77-8 


78-7 


79-6 


80-5 


81-5 


82-4 


83'3 


83-8 


84-3 


847 


85-2 


98 


74-0 


74'9 


75-8 


76-7 


77-6 


78-5 


79-4 


80-3 


8i'3 


82-2 


83-2 


837 


84-2 


84-6 


85-1 


I'OO 


737 


74-6 


75'5 


76-4 


77'3 


78-3 


79'2 


80- 1 


81-1 


82-1 


83-1 


83-5 


84-0 


84'5 


85-0 


1-02 


73*4 


74'3 


75'2 


76-1 


77-1 


78-0 


79*o 


80-0 


80-9 


81-9 


82-9 


83-4 


83-9 


84-4 


84-9 


1-04 


73'i 


74-0 


74'9 


75'9 


76-8 


77-8 


78-8 


79-8 


80-8 


81-8 


82-8 


83-3 


83-8 


843 


84-8 


I -06 


72-8 


737 


747 


75'6 


76-6 


77-6 


78-6 


79-6 


80-6 


8r6 


82-6 


83-2 


837 


84-2 


847 


I -08 


72*5 


73'4 


74'4 


75'4 


76-3 


77' 3 


78-4 


79'4 


80-4 


8r 5 


82-5 


83-0 


83-6 


84-1 


84-6 






56 
Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 

Azimuth is named N or S according to the name of the A and B correction. 



AandB 
Cor- 
rection. 


73 


LATITUDES. 


74 75 76 


77 


78 79 80 81 


82 


83 83$ 


84 i 84i 


85 


AZIMUTHS. 


, 


o 





o 


o 


o 


o 











o 


o 


o 


o 


o 


o 


08 


72'5 


73'4 


74'4 


75'4 


76-3 


77'3 


78-4 


79-4 


80-4 


81-5 


82-5 


83-0 


83-6 


84- r 


84-6 


10 


72-2 


73'i 


74'i 


75'I 


7 6-I 


77-1 


78-1 


79*2 


80-2 


81-3 


82-4 


82-9 


83H 


84-0 


84-5 


20 


70-7 


71-7 


727 


73-8 


74'9 


76-0 


77-1 


78-2 


79'4 


80-5 


817 


82-3 


82-9 


83H 


84-0 


30 


69-2 


7'3 


71-4 


72-5 


737 


74'9 


76-1 


77*3 


78-5 


797 


81-0 


81-6 


82-3 


82-9 


83-5 


40 


67-7 


68-9 


70-1 


71-3 


72-5 


73-8 


75-o 


76-3 


77-6 


79-0 


80-3 


81-0 


817 


82-4 


83-0 


50 


66-3 


67-5 


68-8 


70-1 


71-4 


727 


74-0 


75'4 


76-8 


78-2 


79-6 


80-4 


8ri 


81-8 


82-6 


60 


64-9 


66-2 


67-5 


68-8 


70-2 


71-6 


73'0 


74*5 1 75'9 


77'4 


79-0 


797 


80-5 


8i'3 


82-1 


70 


63-6 


64-9 


66-3 


67-6 


69-1 


70-5 


72-0 


73'6 


75'i 


767 


78-3 


79-1 


79'9 


807 


81-6 


80 


62-2 


63-6 


65*0 


66-5 


68-0 


69-5 


71-0 


72-6 


74'3 


75'9 


77-6 


78-5 


79'3 


80-2 


8r* 


90 


60-9 


62-4 


63-8 


65-3 


66-9 


68-4 


70-1 


71-7 


73'4 


75-2 


77-0 


77'9 


78-8 


797 


80-6 


2*00 


597 


61-1 


62-6 


64-2 


65-8 


67-4 


69-1 


70-8 


72-6 


74'4 


76-3 


77-2 


78-2 


79-1 


80- 1 


2*IO 


58-5 


59'9 


6r 5 


63-1 


647 


66-4 


68-2 


70*0 


71-8 


737 


75-6 


76-6 


77-6 


78-6 


79-6 


2'2O 


57'3 


58-8 


60-3 


62'O 


637 


65-4 


67-2 


69-1 


71-0 


73'0 


75-0 


76-0 


77-0 


78-1 


79-1 


2-30 


56-1 


57'6 


59*2 


60-9 


62-6 


64-4 


66-3 


68-2 


70-2 


72-2 


74*3 


75'4 


76-5 


77-6 


787 


2'4O 


54'9 


56-5 


58-2 


59'9 


61-6 


63-5 


65-4 


67-4 


69-4 


7 J> 5 


737 


74-8 


75'9 


77-0 


78-2 


2-50 


53-8 


55'4 


57*i 


58-8 


60-6 


62-5 


64-5 


66-5 


68-6 


70-8 


73*i 


74-2 


75'4 


7^5 


777 


2-60 


52-8 


54'4 


56-1 


57'8 


597 


61-6 


63-6 


657 


67-9 


70-1 


72-4 


73'6 


74-8 


76-0 


77'2 


2'7O 


5i'7 


53'3 


55'i 


56-8 


58-7 


60-7 


62-7 


64-9 


67-1 


69-4 


7 r8 


73-0 


74*2 


75'5 


76-8 


2'80 


57 


52-3 


54' i 


55'9 


57*8 


59-8 


6i'9 


64-1 


66-3 


68-7 


71-2 


72-4 


737 


75'o 


76-3 


2'QO 


497 


5i'4 


53'i 


54*9 


56-9 


58-9 


6ro 


63-3 


65-6 


68-0 


70-5 


71-8 


73' 1 


74'5 


75-8 


3'00 


487 


50-4 


52-2 


54' 


56-0 


58-0 


60-2 


62-5 


64-9 


67-3 


69-9 


71-2 


72-6 


74-0 


75'3 


3 -IO 


47-8 


49'5 


5^3 


53'i 


55'i 


57'2 


59'4 


61-7 


64-1 


66-7 


69-3 


707 


72-0 


73'5 


74'9 


3 -20 


46-9 


48-6 


50-4 


52-3 


54*3 


56-4 


58-6 


60-9 


63-4 


66-0 


687 


70-1 


7i'5 


72-9 


74*4 


3'30 


46-0 


477 


49'5 


5i'4 


53'4 


55'5 


57-8 


60-2 


62*7 


65-3 


68-1 


69-5 


71-0 


72-4 


74-0 


3-40 


45'2 


46-9 


487 


50*6 


52-6 


547 


57-0 


59'4 


62'0 


647 


67-5 


68-9 


70-4 


72-0 


73'5 


3'50 


44'3 


46-0 


47-8 


497 


51-8 


54' 


56-3 


587 


61-3 


64-0 


66-9 


68-4 


69-9 


7i'5 


73'0 


3-60 


43'5 


45'2 


47-0 


48-9 


51-0 


53'2 


55'5 


58-0 


60-6 


63H 


66-3 


67-8 


69-4 


71-0 


72-6 


3-70 


42-8 


44 '4 


46-2 


48-2 


50-2 


52H 


54-8 


57'3 


59*9 


62-8 


657 


67-3 


68-9 


70-5 


72-1 


3'80 


42-0 


437 


45'5 


47'4 


49'5 


5i7 


54*i 


56-6 


59'3 


62-1 


65-2 


667 


68-3 


70-0 


717 


3-90 


41*3 


42-9 


447 


467 


48-7 


51-0 


53'3 


55'9 


58-6 


61-5 


64-6 


66-2 


67-8 


69'5 


71-2 


4'00 


4'5 


42-2 


44' 


45'9 


48-0 


50'3 


52-6 


55-2 


58-0 


60-9 


64*0 


65-6 


67-3 


69^0 


70-8 


4-10 


39'8 


4i'5 


43'3 


45'2 


47'3 


49-6 


52-0 


54-6 


57'3 


60-3 


63-5 


65-1 


66-8 


68-5 


70-3 


4'20 


39'2 


40-8 


42-6 


44'5 


46-6 


48-9 


5i-3 


53*9 


56-7 


597 


62-9 


64-6 


66-3 


68-1 


69-9 


4*30 


38-5 


40-2 


41-9 


43'9 


46*0 


48-2 


50-6 


53 - 3 


56-1 


59'i 


62-3 


64-0 


65-8 


67-6 


69-5 


4-40 


37'9 


39'5 


4 r '3 


43'2 


45'3 


47'5 


50-0 


52-6 


55'5 


58-5 


6r8 


63-5 


65-3 


67-1 


69 o 


4'50 


37-2 


38-9 


40-6 


42-6 


447 


46-9 


49' 3 


52-0 


54'9 


57 '9 


61-3 


63-0 


64-8 


667 


68-6 


4'6o 


36-6 


38-3 


40-0 


41-9 


44-0 


46-3 


487 


5i-4 


54*3 


57'4 


60-7 


62-5 


64-3 


66-2 


68-2 


4-70 


36-0 


377 


39'4 


4i-3 


43'4 


457 


48-1 


50-8 


537 


56-8 


60-2 


62'O 


63-8 


657 


677 


4-80 


35'5 


37' 1 


38-8 


4<>7 


42-8 


45'i 


47'5 


50-2 


53'i 


56-3 


597 


61-5 


63H 


65-3 


67-3 


4-90 


34'9 


36-5 


38-3 


40-2 


42-2 


44'5 


46-9 


49-6 


52-5 


557 


59*2 


61*0 


62-9 


64-8 


66*9 


5-00 


34'4 


36-0 


377 


39-6 


41-6 


43'9 


46-3 


49-0 


52-0 


55'2 


58-6 


60-5 


62-4 


64-4 


66-5 


5-20 
5'40 


33'3 
32-3 


34'9 
33'9 


36-6 
35'6 


38-5 
37'4 


4<>'5 
39'5 


42-8 
417 


45'2 
44-1 


47*9 
46-8 


50-9 
49-8 


54'i 
53*i 


57'6 
567 


59*5 
58-6 


61-5 
60-6 


63-5 
62-6 


65-6 
64-8 


5'6o 


3i'4 


32-9 


34'6 


36-4 


38-4 


4<>7 


43'i 


45-8 


48-8 


52-1 


557 


57'6 


597 


6i'8 


64*0 


5-8o 


30-5 


32'0 


337 


35'5 


37'5 


397 


42-1 


44-8 


47-8 


5i-i 


547 


567 


58-8 


60*9 


63-2 


6'oo 


297 


31-2 


32-8 


34'6 


36-5 


387 


41-1 


43-8 


46-8 


50-1 


53'8 


55-8 


57'9 


60* i 


62-4 


6'2O 


28-9 


3'3 


3i'9 


337 


35-6 


37-8 


40-2 


42-9 


45'9 


49-2 


52-9 


54*9 


57'i 


59*3 


6i'6 


6-40 


28-1 


29-5 


31-1 


32-9 


34-8 


36-9 


39'3 


42-0 


45'0 


48-3 


52-0 


54'i 


56-2 


58'5 


6o'8 


6-60 


27-4 


28-8 


3'3 


32-1 


34' 


36-1 


38-5 


4 ri 


44-1 


47'4 


5i'2 


S3' 2 


55'4 


577 


6o'i 


6-80 


26-7 


28-1 


29-6 


3i-3 


33'2 


35'3 


37-6 


40'3 


43'2 


46-6 


50'4 


52-4 


54* 6 


56-9 


59*3 


7-00 


26-0 


27-4 


28-9 


30-6 


32-4 


34'5 


36-8 


39'4 


42*4 


457 


49'5 


51-6 


53'8 


56-1 


58-6 


7-20 


25'4 


26-7 


28-2 


29-9 


317 


337 


36-1 


387 


41-6 


44*9 


487 


50-8 


53*o 


55*4 


57'9 


7-40 


24-8 


26-1 


27-6 


29-2 


31-0 


33'o 


35'3 


37'9 


40-8 


44-2 


48-0 


50-0 


52-3 


547 


57*2 


7-60 


24'2 


25'5 


26-9 


28-5 


3'3 


32-3 


34-6 


37-2 


40*1 j 43-4 


47*2 


4f3 


5i'5 


53'9 


56-5 


7-80 


237 


24-9 


26-4 


27-9 


297 


3i7 


33'9 


36-4 


39'3 


427 


46-5 


48-6 


50-8 


53'2 


55'8 






I 


i 











56 
Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION. 
Azimuth is named N or S according to the name of the A and B correction. 



AandB 
Cor- 
rection. 


LATITUDES. 


73 


74 


75 


76 


. 


78 


79 I 80 


81 


82 


83 


83i 


84 


84*' 


85 


AZIMUTHS. 


t 


o 





Q 


o 


o 


o 


o 


o 





o 


o 


o 


o i o 





8-0 


23-I 


24-4 


25'8 


27'3 


29'I 


31'0 


33*2 


357 


3 8'6 


41-9 


457 


47'8 


50'I 


52-5 


55-1 


8'2 


22-6 


23-9 


25-2 


26-8 


28-5 


3'4 


32-6 


35'i 


37'9 


41-2 


45'o 


47-1 


49'4 


51-8 


54*4 


8-4 


22'2 


23H 


247 


26-2 


27-9 


29-8 


32-0 


34'4 


37'3 


40-5 


44'3 


46-4 


487 


51-2 


53-8 


8-6 


217 


22'9 


24-2 


257 


27-3 


29-2 


3i'4 


33-8 


36-6 


39-9 


437 


45-8 


48-0 


50-5 


53'i 


8-8 


21'2 


22'4 


237 


25-2 


26-8 


287 


30-8 


33'2 


36*0 


39-2 


43'o 


45'i 


47'4 


49'9 


52'5 


9-0 


20-8 


22'O 


23-2 


247 


26-3 


28-1 


30-2 


32-6 


35'4 


38-6 


42-4 


44*5 


467 


49'2 


5i-9 


9-2 


20-4 


21'5 


22-8 


24*2 


25-8 


27-6 


297 


32-0 


34-8 


38-0 


417 


43-8 


46-1 


48-6 


5i'3 


9'4 


2O'O 


2I'I 


22'3 


237 


253 


27-1 


29-1 


3i*5 


34'2 


37-4 


41-1 


43'2 


45*5 


48-0 


507 


9-6 


ig'6 


20'7 


21*9 


233 


2 4 -8 


26-6 


28-6 


31-0 


337 


36-8 


40-5 


42-6 


44'9 


47'4 


50-1 


9-8 


19-2 


20'3 


21-5 


22-9 


24-4 


26-1 


28-1 


30-4 


33'i 


36-2 


39'9 


42-0 


44'3 


46-8 


49'5 


IO'O 


18-9 


19-9 


2I'I 


22-5 


24-0 


257 


277 


29-9 


32-6 


357 


39'4 


4!'5 


437 


46-2 


48-9 


IO'2 


18-5 


I9*6 


20'7 


22*1 


23*5 


25-2 


27-2 


29-4 


32-1 


35'2 


38-8 


40-9 


43'2 


45-6 


4 8- 4 


IO- 4 


18-2 


19-2 


20' 4 


217 


23-I 


24-8 


267 


29-0 


31-6 


34-6 


38'3 


40-3 


42-6 


45' i 


47-8 


io'6 


17-9 


l8'9 


2O'I 


21'3 


22-8 


24-4 


26-3 


28-5 


3i'i 


34*i 


377 


39'8 


42-1 


44'5 


47'3 


10-8 


17-6 


18-6 


197 


2O'9 


22'4 


24-0 


25*9 


28-1 


30-6 


33'6 


37*2 


39'3 


4I-5 


44-0 


467 


II'O 


17*3 


1*3 


19-4 


20-6 


22'O 


23-6 


25'5 


27-6 


30-2 


33'2 


367 


38-8 


41-0 


43'5 


46-2 


II'2 


17-0 


17-9 


I9'O 


20-3 


21'6 


23-2 


25-1 


27-2 


297 


327 


36-2 


38-3 


40-5 


43'o 


457 


11-4 


167 


17-7 


18-7 


19-9 


21'3 


22-9 


247 


26-8 


293 


32-2 


357 


37-8 


40-0 


42-5 


45'2 


n-6 


16-4 


i7'4 


18-4 


19-6 


2I'O 


22-5 


24-3 


26-4 


28-9 


31-8 


35'3 


37'3 


39'5 


42-0 


447 


ii-8 


16-2 


17-1 


18-1 


I9-3 


20-6 


22'2 


23-9 


26-0 


28-4 


3i'3 


34-8 


36-8 


39-0 


4i'5 


44-2 


I2'0 


15-9 


16-8 


17-8 


19-0 


20'3 


21'8 


23-6 


25-6 


28-0 


30-9 


34'4 


36-4 


38-6 


41-0 


437 


12*2 


157 


16-6 


17-6 


187 


2O'O 


21'5 


23-2 


25-3 


277 


30-5 


33'9 


35'9 


38-1 


40-5 


43'2 


I2- 4 


15-4 


16-3 


I7'3 


18-4 


197 


21'2 


22'9 


24-9 


27-3 


30-1 


33-5 


35'5 


377 


40-1 42-8 


I2'6 


15-2 


16-1 


17-0 


18-2 


19-4 


2O'9 


22-6 


24-6 


26-9 


297 


33*i 


35'o 


37'2 


39'6 


42-3 


I2'8 


15-0 


15-8 


16-8 


17-9 


19-2 


20'6 


22'3 


24-2 


26-5 


29-3 


327 


34'6 


36-8 


39'2 


41-9 


I3-0 


14-7 


15-6 


16-6 


17-6 


18-9 


20'3 


22*O 


23-9 


26-2 


28-9 


32-3 


34*2 


36-3 


387 


41-4 


I3-2 


M'5 


I5H 


16-3 


17-4 


18-6 


20-0 


21'7 


23-6 


25-8 


28-6 


3i'9 


33-8 


35'9 


38-3 


41-0 


i3'4 


H'3 


i5'i 


16-1 


17-1 


18-4 


197 


2I- 4 


23*3 


25'5 


28-2 


3^5 


33'4 


35'5 


37'9 


40-6 


I3'6 


14-1 


14-9 


I5'9 


16-9 


18-1 


I9'5 


2I'I 


22-9 


25-2 


27-8 


31-1 


33'0 


35'i 


37'5 


40-2 


I3'8 


I3-9 


14-7 


I5'6 


167 


17-9 


I9-2 


20'8 


227 


24-9 


27-5 


307 


32-6 


347 


3/-i 


397 


14-0 


137 


*4'5 


J 5'4 


16-5 


17-6 


i9'O 


20'5 


22' 4 


24-5 


27-2 


30-4 


32-3 


34'3 


367 


39'3 


14-2 


I3-5 


i4'3 


I5'2 


16-2 


17-4 


187 


20-3 


22'I 


24-2 


26-8 


30-0 


3i'9 


34'0 


36-3 


38-9 


14-4 


I3-4 


14-1 


15-0 


16*0 


17-2 


18-5 


20'O 


21'8 


23-9 


26-5 


297 


3i'5 


33'6 


35'9 


38-5 


14-6 


13-2 


14-0 


14-8 


15-8 


i6'9 


18-2 


197 


21'5 


23-6 


26-2 


29-3 


31-2 


33'2 


35-6 


38-2 


14-8 


13-0 


i3'8 


14-6 


i5'6 


167 


18-0 


I9-5 


21-3 


23-4 


25'9 


29-0 


30-8 


32-9 


35'2 


37-8 


15-0 


I2'8 


13-6 


14-4 


!5'4 


16-5 


17-8 


I9-3 


2I'O 


23-1 


25-6 


287 


30-5 


32-5 


34-8 


37'4 


15-2 


127 


I3-4 


i4'3 


15-2 


16-3 


17-6 


I9'O 


2O'8 


22-8 


25'3 


28-4 


30-2 


32'2 


34'5 


37-0 


*5'4 


12-5 


I3'3 


14-1 


15*0 


16-1 


i7'3 


18-8 


20'5 


22'5 


25-0 


28-0 


29-8 


3i'8 


34'i 


367 


15-6 


12-4 


I3'i 


I3-9 


I4-* 


I5-9 


17-1 


18-6 


20-3 


22'3 


247 


277 


29-5 


3i'5 


33-8 


36-3 


i5'8 


I2'2 


12-9 


137' 


147 


157 


i6'9 


18-4 


2O'0 


22'O 


24*5 


27-4 


29-2 


31-2 


33'4 


36-0 


16-0 


I2'I 


12-8 


13-6 


I4-5 


I5-5 


167 


18-1 


19-8 


21-8 


24-2 


27-2 


28-9 


30-9 


33'i 


35-6 


16-2 


11-9 


I2'6 


i3'4 


H'3 


I5'3 


16-5 


17*9 


19-6 


21'5 


23-9 


26-9 


28-6 


30-6 


32-8 


35'3 


16-4 


n-8 


12-5 


13*3 


14-1 


15-2 


16-3 


177 


I93 


20'3 


237 


26-6 


28-3 


30-3 


32-5 


35'o 


16-6 


n-6 


12-3 


13-1 


14-0 


15-0 


16-2 


17*5 


19-1 


2I'I 


23H 


26-3 


28-0 


30-0 


32-2 


347 


16-8 


"5 


I2'2 


13-0 


13-8 


14-8 


16*0 


i7'3 


18-9 


20'8 


23-2 


26'O 


277 


297 


31-8 


34'3 


17-0 


11-4 


I2'0 


12-8 


137 


147 


i5'8 


17-1 


187 


2O'6 


22-9 


25-8 


27-5 


29H 


3i 5 


34'0 


17-2 


II'2 


11-9 


127 


I3'5 


&T5 


15-6 


16-9 


18-5 


20- 4 


227 


25'5 


27-2 


29-1 


31-2 


337 


17-4 


II'I 


n-8 


12-5 


i3'4 


i4'3 


I5-5 


16-8 


18-3 


20'2 


22-4 


25-2 


26 :g 


28-8 


30-9 


33'4 


17-6 


II'O 


u-6 


12-4 


13-2 


14-2 


i5'3 


16-6 


18-1 


2O'O 


22'2 


25-0 


267 


28-5 


307 


33' 1 


17-8 


io'9 


"'5 


I2'2 


13-1 


14-0 


15-1 


16-4 


17-9 


I9'8 


22'O 


247 


26-4 


28-3 


30-4 


32-8 


18-0 


10-8 


11-4 


I2'I 


12-9 


13*9 


15-0 


16-2 


177 


19-6 


21-8 


24*5 


26-1 


28-0 


30-1 


32-5 


18-2 


io'6 


11-3 


I2*O 


12-8 


137 


14-8 


16-1 


17-6 


19-4 


21-5 


24'3 


25-9 


277 


29-8 


32-2 


18-4 


10-5 


11*2 


11-9 


127 


13-6 


14-6 


I5-9 


17-4 


19-2 


21'3 


24*0 


25-6 


27-5 


29'6 


3I-9 


18-6 


10-4 


II'O 


117 


12-5 


I3H 


i4'5 


157 


17-2 


19-0 


2I'I 


23-8 


25-4 


27-2 


29-3 


317 


18-8 


10-3 


10-9 


ix-6 


12-4 


I3-3 


14*3 


15-6 


17-0 


18-8 


20'9 


23-6 


25-2 


27-0 


29-0 


3i'4 



57 



Table C. 

AZIMUTHS CORRESPONDING TO THE A AND B CORRECTION 
Azimuth is named N or S according to the name of tha A and B correction. 



AandB 


LATITUDES. 


Cor- 






























rection. 


73 


74 


75 


76 


77 


78 


79 


80 


81 


82 


83 


83* 


84 I 84 


85 






AZIMUTHS. 


19-0 


IO'2 


I0'8 


"5 


12-3 


13*2 


14-2 


15-4 


16-9 


18-6 


20'7 


23*4 


24-9 


267 


28-8 


31*1 


19-2 


lO'I 


10-7 


11-4 


I2'I 


13*0 


14-1 


I5-3 


167 


iS-4 


20-5 


23*1 


247 


26-5 


28-5 


30-9 


19-4 


10-0 


io-6 


11-3 


I2'O 


12-9 


I 3'9 


I5"I 


16-5 


18-2 


20'3 


22-9 


24*5 


26-2 


28-3 


30-6 


19-6 


9-9 


10-5 


11*2 


1 1 '9 


12-8 


13-8 


15-0 


16-4 


18-1 


20' I 


22-7 


24-3 


26*0 


28-0 


3'3 


19-8 


9-8 


10-4 


II'O 


n-8 


12-7 


137 


14-8 


16-2 


17-9 


I9'9 


22-5 


24-0 


25*8 


27-8 


30-1 


2O'O 


97 


10-3 


io9 


117 


12-5 


13-5 


14-7 


16-1 


177 


I9'8 


22-3 


23-8 


25-6 


27*5 


29-8 


2I'O 


9'3 


9-8 


10-4 


ii'i 


I2'O 


12-9 


I 4 '0 


15-3 


16*9 


18-9 


21-3 


22-8 


24'5 


26-4 


28-7 


22-0 


8-8 


9'4 


10-0 


10-6 


II'4 


12-3 




147 


16-2 


18-1 


20-5 


21-9 


23*5 




27*5 


23-0 


8'5 


9-0 


9-5 


IO'2 


10*9 


ii-8 


12-8 


14-1 


I 5'5 


I 7'3 


19-6 


2I'O 


22'6 


24-4 


26-5 


2 4 '0 


8-1 


8-6 


9-1 


9-8 


10-5 


n*3 


I2- 3 




14-9 


167 


18-9 


2O'2 


21'7 




25*6 


25-0 


7-8 


8'3 


8-8 


9'4 


lO'I 


10-9 


n-8 


13-0 


X 4'3 


i6'o 


18-2 


I9'5 


20'9 


22-6 


247 


26-0 


7'5 


7-9 


8*5 


9-0 


97 


10-5 


11-4 


12-5 


13*8 


*5'4 


17*5 


18-8 


2O'2 


21-9 


23*8 


27-0 


7-2 


77 


8-x 


87 


9*3 


lO'I 


II'O 


I2'O 


I3-3 


14-9 


16-9 


18-1 


J 9'5 




23*0 


28-0 


7-0 


7*4 


7'9 


8-4 


9-0 


97 


10-6 


n-6 


12-9 


14-4 


16-3 


17*5 


18-9 


20-4 




29-0 


67 


7-1 


7-6 




87 


9'4 


IO'2 


II'2 


12-4 


I3-9 




16-9 


18-3 


I9'8 


21-6 


30-0 


6'5 


6-9 


7*3 


7-8 


8-4 


9-1 


9'9 


IO'9 


I2'O 


13*5 


15.3 


16-4 


177 


19*2 


20-9 


31-0 


6'3 


67 


7-1 


7-6 


8'2 


8-8 


9-6 


10-5 


117 


13-0 


14-8 


15-9 


17-2 


18-6 


20-3 


3 2-0 


6-i 




6-9 


7*4 


7-9 


8-5 


9*3 


IO'2 


ii'3 


127 


14-4 


I 5"4 


16-6 


18-1 


19-7 




5*9 


6-3 


67 




77 




9-0 


9'9 


II'O 


12-3 


14-0 


15-0 


16-2 


17-5 


19-2 


34' 


57 


6-1 


6-5 


6-9 


7*4 


8-i 


8-8 


9-6 


io'6 


11-9 


13-6 


14-6 


157 


17-1 


18-6 


35'0 


5*6 


5'9 


6'3 


67 


7-2 


7-8 


8'5 


9'3 


10-4 


n-6 


13*2 


14-2 


15-3 


16-6 


18-2 


36-0 


5*4 


5 '8 


6-1 


6-6 


7-0 


7'6 




9-1 


lO'I 


11-3 


12-8 


i 3 ' 8 


14-9 


l6'2 


177 


37'o 


5'3 




6-0 


6-4 


6-9 


7'4 


8-i 


8-8 


9-8 


II'O 


12-5 




14*5 


157 


17-2 


38-0 


5*1 


5*5 


5*8 


6'2 


67 


7-2 


7*9 


8-6 


9*5 


107 


I2'2 


13-1 


14-1 




16-8 


40-0 


4'9 




5*5 


5*9 


6-3 


6-9 


7*5 


8-2 


9-1 


IO-2 


n-6 


12-5 


13*5 


14-6 


i6'o 


42-0 


47 


4*9 


5*3 


5-6 


6'0 


6'5 


7-1 


7-8 


87 


97 


II'I 


ii'9 


I2'8 


14-0 


I5-3 


44-0 


4*4 


47 


5*0 


5*4 


5 '8 


6'2 


6-8 


7*5 


8-3 


9*3 


10-6 


11-4 


12-3 


13*3 


14-6 


46-0 


4*3 


4'5 


4-8 




5*5 


6-0 


6*5 


7-1 


7-9 


8-9 


lO'I 


10-9 


117 


I2'8 


14-0 


48-0 




4'3 




4*9 


5*3 


57 


6'2 


6-8 


7-6 




97 


10-4 




12-3 


13*4 


50*0 


3'9 


4-2 


4*4 


47 




5'5 


6-0 


6-6 


7'3 


8'2 


9'3 


10-0 


I0'8 


ii'8 


12-9 


52-0 


3-8 


4-0 


4-2 


4'5 


4'9 


5'3 


5*8 


6-3 


7-0 


7-9 


9-0 


9-6 


10-4 


11-3 


12-4 




3-6 






4'4 


47 




5*5 


6'i 


6-8 


7'6 


8-6 


9*3 


IO'O 


10*9 


12-0 


56-0 


3 5 


37 


3'9 




4*5 


4*9 


5*3 


5'9 


6*5 


7'3 


8*3 


9-0 


97 


10-6 


n-6 


58-0 


3*4 


36 






4*4 


47 




57 




7-1 




7 


9*4 






60-0 


33 


3*5 


37 


3*9 


4-2 


4-6 


5*o 


5'5 


6-i 


6-8 


7-8 


8-4 


9-1 


9*9 


io-8 


62-0 


3*2 


3'3 


3-6 


3-8 


4' 1 


4'4 


4-8 


5*3 


5*9 


6-6 


7*5 


8-1 


8-8 


9-6 


io'5 


64-0 


3* 1 




3'5 


37 


4-0 


4'3 


47 


5' 1 


57 


6-4 


7'3 


7-9 


8*5 


9*3 


IO-2 


66-0 


3'0 


3'i 


3'4 


3-6 


3'9 


4-2 


4*5 


5*o 


5*5 


6'2 


7-1 


7-6 


8'2 


9-0 


9'9 


68-0 


2-9 




3-3 


3*5 


37 




4'4 


4-8 


5'4 


6-0 


6-9 


7'4 


8-0 


87 


9'6 


70-0 


2-8 


3-0 


3*2 


3*4 


3-6 


3'9 


4'3 


47 


5*2 


5'9 


67 


7-2 


7-8 


8*5 


9*3 


80-0 


2*4 


2-6 


2'8 


3-0 


3*2 


3'4 


37 


4-1 


4-6 


5-1 


5*9 


6-3 


6-8 


7*4 


8-2 


90-0 


2*2 


2-3 


2-5 


2-6 


2-8 




3*3 


37 


4-1 


4-6 


5*2 


5*6 


6* i 


6-6 


7'3 


100-0 


2'O 




2'2 


2-4 


2-5 


2-8 


30 


3'3 


37 


4* 1 


47 


5* 


5*5 


6'o 


6*5 


I2O-O 


1-6 


17 


i-8 


2-O 


2'I 


2-3 




27 


3-0 


3*4 


3'9 


4-2 


4-6 


5* 


5'5 


I4O-O 


i'4 




1-6 


I'7 


i'8 


2'O 


2-1 


2-4 


2'6 


2-9 


3*4 


3-6 


3'9 


4*3 


47 


1 60-0 


I'2 


1 '3 


**4 


i*5 


1-6 


I'7 


1-9 


2-1 


2-3 


2-6 


2-9 


3*2 


3*4 


37 


4'i 


1 80-0 


I'l 




I'2 


1 '3 


x '4 


i5 


17 


1-8 


2-0 


2-3 


2'6 


2'8 


3*o 


3'3 


3*6 


20O-O 


I'O 


I'O 


I'l 


1*2 


1*3 


*"4 




1-6 


1-8 


2*1 


2-3 


2*5 


27 


3-0 


3*3 


3OO-O 




07 




0-8 


0-8 


0-9 


I'O 


I'l 


I'2 


I '4 


1-6 


17 


1-8 


2'0 


2-2 


400-0 


'5 


0'5 


0-6 


0-6 


0-6 


07 


0-8 


0-8 


0-9 


I'O 


I'2 


1-3 


*'4 


1*5 


1-6 


500-0 


0-4 


0-4 


0-4 


'5 


o*5 


0-6 


0-6 


0-7 


07 


0-8 


0-9 


I'O 


1*1 


I '2 


1*3 


6OO-0 


0-3 


0-3 




0-4 


0-4 


0*5 


"5 




0-6 


0-7 


0-8 


0-8 


0-9 


I'O 


i'i 


700-0 
800-0 


O'2 


0-3 
0-3 


0'3 
0-3 


0'3 
0-3 


0-4 
0-3 


0-4 
0-3 


0-4 
0-4 


0-4 


0'5 


0-6 


0-7 
0-6 


07 
0-6 


0-8 
07 


0-9 

07 


0-9 
0-8 


1000-0 


0'2 


O'2 


O-2 


0'2 




0-3 


0-3 


0-3 


0-4 


0-4 


o-5 


o*5 


o*5 


0-6 


0-7 



58 

Traverse Table. 

SHOWING DIFFERENCE OF LONGITUDE AND CORRESPONDING DEPARTURE. 



4J 

3 


DIFFERENCE OF LONGITUDE. 


10 


11 


12 


13 


14 


15 -16 -17 


18 -19 


20 


21 -22 


23 


24 


25 


o 


























2 


TOO 


no 


120 


130 


140 


1501 -160 


170 -i 80 -190 


200 


210 -220 


230 


240 


250 


4 


100 


no 


120 


130 


140 


150 -160 


170 


loo -190 


200 


209 -219 


229 


239 


249 


6 


099 


109 


119 


129 


139 


1491-159 


169 


179 -189 


199 


2O9 -219 


229 


239 


249 


8 


099 


109 


119 


129 


139 


148 -158 


168 


178 -188 


I 9 8 


208 -218 


228 


238 


248 


10 


-098 


108 


118 


128 


138 


148 -158 


167 


1771-187 


197 


207 -217 


227 


236 


246 


n 


098 


108 


118 


128 


137 


147 -157 


167 


177 -187 


196 


206 -216 


226 


236 


245 


12 


098 


108 


117 


127 


137 


147 -157 


166 


176 -186 


196 


205|'2I5 


225 


235 


245 


*3 


097 


107 


117 


127 


136 


146 -156 


166 


175 -185 


195 


205-214 


224 


234 


244 


I 4 


097 


107 


116 


126 


136 


146 -155 


165 -175 


-184 


194 


204 -213 


223 


233 


243 


*5 


097 


106 


116 


126 


135 


145 '155 


164 


174 


184 


193 


203; -213 


222 


232 


241 


16 


096 


106 


ii5 


125 


135 


J 44 -154 


163 


173 


183 


192 


202J -211 


221 


231 


240 


17 


096 


105 


115 


124 


134 


I43-I53 


163] -172 -182 


191 


201; -210 


220 


230 


239 


18 


095 


105 


114 


124 


133 


I43i'i52 


162) -171 -181 


190 


200J -2O9 


219 


228 


238 


19 


095 


104 


113 


123 


132 


142-151 


161 


170! -r8o 


189 


199' '208 


217 


227 


236 


20 


094 


103 


113 


122 


132 


I4I-I50 


160 


169 -179 


188 


197 


207 


216 


226 


235 


21 


093 


103 


112 


121 


131 


140 -149-159 


168 


177 


187 


I 9 6 


205 


215 


224 


233 


22 


093 


IO2 


III 


121 


130 


139 -148-158 


167 


176 


185 


195 


204 


213 


223 


232 


23 


092 


IOI 


IIO 


120 


129 


138 -147; -156 


166 -175 


184 


193 


203 


212 


221 


230 


2 4 


091 


IOO 


no 


119 


128 


137 


146 


155 


164-174 


183 


192 


201 


210 


219 


228 


25 


091 


100 


109 


118 


127 


136 


J 45 


154 


163 


172 


181 


I9O 


199 


208 


218 


227 


26 


090 


099 


108 


117 


126 


135 


144 


153 


162 


171 


180 


l8 9 


I 9 8 


207 


216 


225 


27 


089 


098 


107 


116 


125 


134 


143 


151 


160 -169 


178 


I87I-I96 


205 


214 


223 


28 


088 


097 


106 


ii5 


124 


132 


141 


150 


159 


168 


177 


I8 5 


194 


203 


212 


221 


29 


087 


9 6 


105 


114 


122 


131 -140 


149 


157 


166 


175 


I8 4 


192 


201 


210 


219 


3<> 


087 


095 


104 


113 


121 


130! -139 


147 


156 


165 


173 


182 


igi 


199 


208 


217 


31 


086 


094 


103 


in 


120 


129-137 


146 


154 


163 


171 


180 


189 


197 


206 


2I 4 


32 


085 


093 


IO2 


IIO 


119 


1271-136 


144 


153 -161 


170 


178 


-I8 7 


195 


20 4 


212 


33 


084 


092 


IOI 


109 


117 


126 


134 


H3 


151 


159 


168 


176 


-I8 5 


193 


2OI 


210 


34 


083 


091 


099 


108 


116. 


124 


133 


141 


149 


158 


166 


174 


182 


191 


199 


207 


35 


082 


090 


098 


106 


115 


123 


*3* 


139 


147 


156 


164 


172 -180 


188 


197 


205 


36 


081 


089 


097 


105 


113 


121 


129 


138 


146 


154 


162 


170-178 


186 


194 


202 


37 


080 


088 


096 


104 


112 


I 2O 


128 -136 


144 


152 


160 


168 -176 


184 


192 


2OO 


38 


079 


087 


095 


102 


IIO 


118 


126 


134 


142 -150 


158 


165 -173 


181 


I8 9 


197 


39 


078 


085 


093 


IOI 


109 


117 


124 


132 


140 -148 


155 


163 -171 


179 


187 


194 


40 


077 


084 


092 


IOO 


107 


115 


123 


130 


138 -146 


153 


161 


I6 9 


176 


I8 4 


192 


4 1 


075 


083 


091 


098 


106 


113 


121 


128 


I 3 6| -143 


*5* 


158 


166 


174 


181 


189 


42 


074 


082 


089 


097 


104 


III 


119 


126 


134! -141 


149 


156 


163 


171 


178 


186 


43 


073 


080 


088 


095 


IO2 


IIO 


117 


124 


132 


139 


146 


154 


161 


168 


176 -183 


44 


072 


079 


086 


094 


IOI 


108 


115 


122 


129 


137 


144 


151 -158 


165 


173 


180 


45 


071 


078 


085 


092 


099 


106 


113 


120 


127 


134 


141 


148 


156 


163 


170 


177 


46 


069 


076 


083 


090 


097 


104 


III 


118 


125 


132 


139 -146 


153 


160 


167 


174 


47 


068 


075 


082 


089 


095 


102 


109 


116 


123 


130 


136 -143 -150 


157 


164 


170 


48 


067 


074 


080 


087 


094 


IOO 


107 


114 


120 


127 


134-141 


147 


*54 


161 


6 7 


49 


066 


072 


079 


08 5 


092 


9 8 


I0 5 


112 


118 


125 


131 


138 


144 


151 


157 


164 


50 


064 


071 


077 


084 


090 


096 


I0 3 


109 


116 


122 


129 


135 


141 


148 


154 


161 


5i 


063 


069 


076 


082 


088 


094 


IOI 


107 


113 


120 


126 


132 


138 


145 


151 


157 


52 


062 


068 


074 


080 


086 


092 


099 


I0 5 


in 


117 


123 


129 


135 


142 


148 


J 54 


53 


060 


066 


072 


078 


084 


090 


9 6 


102 


108 


II 4 


120 


126 


132 


138 


144 


150 


54 


059 


065 


071 


076 


082 


088 


094 


ioo| -106 


112 


118 


123 


129 


135 


141 


147 


55 


057 


063 


06 9 


075 


080 


086 


092 


098 


103 


109 


115 


120 


126 


132 


138 


143 


56 


056 -062 


06 7 


073 


078 


084 


089 


095 


IOI 


106 


112 


117 


123 


129 


134 


140 


57 


054 -060 


06 5 


071 


076 


082 


087 


093 


098 


103 


109 


II 4 


I2O 


125 


130 


136 


58 


053 -058 


064 


069 


074 


079 


08 5 


090 


095 


IOI 


106 


III 


117 


122 


127 


132 


59 


052 -057 


O62 


067 


072 


077 


082 


088 


093 


098 


103 


108 


II 3 


118 


124 


129 


60 


050 -055 


060 


06 5 


070 


075 


080 


085 


090 


095 


IOO 


105 


IIO 


115 


I2O 


125 


61 


04? -053 


058 


063 


068 


73 


078 


082 


087 


092 


097 


102 


107 


112 


116 


121 


62 


047 -052 


056 


061 


066 


070 


075 


080 


085 


089 


094 


099 


103 


108 


113 


117 


63 


045 


050 


054 


059 


064 


068 


>:> 73 


077 


082 


086 


091 


095 


IOO 


104 


109 


II 3 


64 


44 


048 


053 


057 


061 


066 


070 


075 


079 


083 


088 


O92 


096 


IOI 


105 


IIO 


65 


0421 -046 


051 


055 


059 


063 


058 


072 -076 


080 


085 


089 ; -093 


097 


IOI 


106 




1 










' 













59 
Traverse Table. 

SHOWING DIFFERENCE OF LONGITUDE AND CORRESPONDING DEPARTURE. 



$ 


DIFFERENCE OF LONGITUDE. 














1 






26 


27 


28 


29 


30 


31 


32 -33 


34 -35 


36 


37 1 -38 


39 


40 


o 
















i 






2 


260 -270 


280 -290 


300 


310 -320 -330 


34 -350 


360 


; .370 -380 


390 


400 


4 


259 -269 


279 -289 


299 


39 -319 


329 


339 -349 


359 


369; -379 


389 


399 


6 


259 -269 


278 -288 


298 


308 


318 


328 


338 -348 


358 


368; -378 


388 


398 


8 


257, -267 


277 -287 


297 


307 


317 


327 


337J '347 


356 


366 -376 


386 


396 


10 


256 -266 


276 


286 


295 


305 


315 


325 


335 


345 


355 


364! '374 


384 


394 


n 


255 -265 


275 


285 


294 


34 


3*4 


324 


334 


344 


353 


363 '373 


383 


'393 


12 


2541 -264 


274 -284 


293 


303 


3 J 3 -323 


333 


342 


352 


.362 -372 


381 


391 


13 


253 


263 


273! -283 


292 


302; -312 -322 


331 -341 


351 


361 -370 


380 


390 




252 


262 


272 


281 


291 




3101 -320 


33 '34 


349 


359 -369 


378 


388 


15 


251 


261 


270 


280 


290 


299 


309 -319 


328j -338 


348 


357 -367 


377 


386 


16 


250 


260 


269 -279 -288 


298 


38| -317 


327 -336 


346 


356, -365 


375 


385 


17 


249 


258 


268 -277 -287 


296 


306 -316 


325 


335 


344 


354 ! -363 


373 


383 


18 


247 


257 


266 -276 -285 


295 


34 


314 


3231 '333 


342 


352 -361 


371 


380 


19 


246 


255 


265! -274 


284 


293 


303 -312 


321 


331 


340 


35 '359 


369 


378 


20 


244 


254 


263 -273 


282 


291 


301 


310 


319 


329 


338 


348 -357 


366 


376 


21 


243 


252 


261 


271 


280 


289 


299 -308 


317 -327 


336 


345 '355 


364 


373 


22 


241 


250 


260 


269 -278 


287 


297 -306 


315 


325 


334 


343 -352 


362 


371 


23 


239 


249 


258 


267 -276 


285 


295 '34 


313 


322 


331 


34*1 -350 


359 


368 


24 


238 


247 


256 


265 -274 


283 


292 


301 


311 


320 


329 


338 j -347 


356 


365 


25 


236 


245 -254 -263 -272 


281 


290 


299 -308 


317 


326 


335 '344 


353 


363 


26 


234 


243 


252 -261 -270 


279 


288 


297 -306 


315 


324 


333 


342 


351 


360 


27 


232 


241 -249 -258 -267 


276 -285 


294 -303 -312 


321 


33 


339 


347 


356 


28 


230 


238 -247 


256 -265 


274 


283 


291 1.300 -309 


318 


327 


336 


344 


353 


29 


227 


236 


245 


254! -262 


271 


280 


289 -297J '36 




324 


332 -341 


350 


30 


225 


234 


242 


251 


260 


268 


277 


286 -294 -303 


312 


320 


329 -338 


34 6 


31 


223 


231 


240 -249 


257 


266 


274 -283-2911 -300 


309 


317 


326, -334 


343 


S 2 


220 


229 


237 -246 


254 


263 


271 -280 -288 -297 


35 


314 


322 -331 


339 


33 


218 


226 -235! -243 


252 


260 


268 -277 -285 -294 


302 


310 


319 -327 


335 


34 


216 


224 


232 


240 -249 


257 


265 


274 -282 -290 


298 


.307 


315 -323 


332 


35 


213 


221 


229 


238 


246 


254 


262 


270 -279! -287 


295 


303 


311 -319 


328 


36 


210 


218 


227 


235 


243 


251 


259 -267 -275 -283 


291 


299 


307 -316 


324 


37 


208 


216 


224 


232 


240 


248 


256 -264' -272 -280 


288 


295 


'33 '3 11 


319 


38 


205 


213 


221 


229 


236 


244 


252 


260 -268 


276 


284 


292 


299 -37 


315 


39 


202 


2IO 


218 


225 


233 


241 


249 


256 -264 


272 


280 


-288 


295 '33 


3" 


4 


199 


207 


214 


222 


230 


237 


245 


253' -260 -268 


-276 


283 


291 -299 


306 


4 1 


196 


204 


211 


219 


226 


234; -242 


249 -257 -264 


272 


279 


287 -294 


302 


42 


193 


201 


208 


216 


223 


230 


238 


245 -253 


260 


268 


275 


282 -290 


297 


43 


190 


197 


205 


212 


219 


227 


234 


241 


249 -256 


263 


271 


278 -285 


293 


44 


187 -194 


201 


209 


216 


223 -230 


237 -245 


252 


259 


266 


273 


281 


288 


45 


184 -191 


198 


205 


212 


219 


226 


233 -240 


247 


255 


262 


269 


276 


283 


46 


181 


188 


195 


201 


208 


215 -222J -229 


236 


243 


250 


257 


264 


271 


278 


47 


177 -184! -191 


198 


205 


211 


218 -225 


232 


239 


246 


252 


259 


266 


273 


48 


174 -181 


187 


194 


2OI 


207 


2I 4 -221 


228 


234 


241 


248 


254 


261 


268 


49 


171 -177 


184 


190 


197 


203 


2IO[ -216 


223 


230 


236 


243 


249 


256 


262 


50 


167-174 


180 -186 


193 


199 


206 -212 


219 


225 


231 


238 


244 


251 


257 


5 1 


164 -170 


176 -183 


189 


195 -2OI 


208 -214 


220 


227 


233 


239 


245 


252 


52 


160 -166 


172 -179 -185 


191 


197 


203 -209 


215 


222 


228 


234 


240 


246 


53 


156 -162 


169 -175 -181 


187 -193 


199 -205 


211 


217 


223 


229 


235 


241 


54 


153 -I 59 


165 -170 -176 


182 


188 


194 -200 


2O6 


212 


217 


223 


229 


235 


55 


149 -155 


161 


166 -172 


;I 7 8 


184 


189 -195 


2OI 


206 


212 


218 


224 


229 


56 


145 -151 


157 


162 


168 


173 


179 


I8 5 


190 


196 


2OI 


207 


212 


218 


224 


57 


142 -147 


152 


158 


163 


169 


174 


180 -185 


191 


196 


202 


207 


212 


218 


58 
59 


138 -143 
134 ' I 39 


148 
144 


154 
149 


159 
155 


I6 4 

160 


170 
165 


175 -180 -185 
170 -175! -180 


191 
I8 5 


196 -2OI 
191 -196 


207 
2OI 


212 
206 


60 


130 -135 


140 -145 


150 


155 


160 -165 


170 


175 


180 


185 


190 


195 


200 


61 


126 -131 


136 


141 


145 


150 


155 -160 -165 


170 


175 


179 -184 


189 


194 


62 


122 


127 




136 -141 


-146 


150 -155 -160 


I6 4 


169 


174 -178 


183 


188 


63 


118 


123 


127 


132 -136 


141 


145 -150 -154 


159 


163 


168 -173 


177 


182 


64 


114 -118 


123 


127 -132 


136 


140 -145 -149 -153 


158 


162 -167 


171 


751 


65 


no -114 


118 


123! -127 




135 -139 -144 -148 


152 


150 -161 -it>5 


169 




60 
Traverse Table. 

SHOWING DIFFERENCE OF LONGITUDE AND CORRESPONDING DEPARTURE. 



+5 


DIFFERENCE OF LONGITUDE. 




41 


42 -43 -44 -45 


46 -47" 


48 


49 


50 


51 


52 53 


54 


55 


o 












1 


1 2 


410! 


420 


430; -440 -450 


460 


470! -480 


490 


500 


510 -520 . 53 oj -540 -550 


L4 


409 


419 


429' -439 '449 ; 


459 


469 -479 


489 


499 


59 


519 -529 -539, '549 


6 


408 


418 


428' -438 -448 


457 


-467 


477 


487 


497 


57 


517 -527 -537 -547 


8 


406 


416 


426 -436 


446 j 


456 


465 


475 


485 


495 


505 


515 -525 '535 '545 


10 


-404 


414 


423 ;433 


443 S 


453 


463 


473 


483 


492 


502 


512 -522 -532 -542 


ii 


402 


412 


422 -432 -442: 


452 


461 


471 -481 


491 


501 


510 -520 -530 -540 


12 
13 
14 


401 
399 
398 


411 
.409 
408 


421 \ -4301-440: 
419 -429, -438 ,; 
417 -427 '437| 


45 
448 
446 


460 
458 
456! 


470 
468 
466 


479 
477 
475 


489 
487 
485 


499 
'497 
495 


509 -5181 -528 -538 
57! 5 I 6 -526 -536 
505 -514 -524 '534 


15 


396 


406 


415 -425! 


' 435 J 


444 


'454 '4 6 4 


473 


483 


493 


502 -512 -522 -531 


16 


394 


404 


4 I 3j -423 


433 


442 


452 '4 61 


471 


-481 


490 


-500 -509 -519 -529 


17 


392 


402 


4111-421 -430 


.440 


'449i '459 


469 


-478 


488 


'497j '57 


516 -526 


18 


390 


399 


-409' -418 


428 


437 


447 '457 


466 


476 


485 


'495 '54 


5*4 -523 


19 


388 


397 


407 -416 


425 


435 


'444 


454 


463 


473 


-482 


492: -501 


511 -520 


20 


385 


395 


404 -413 


423 


432 


442 


'45 1 


460 


470 


479 


489 -498 -507 -517 
























21 


383 


392 


401 -411 


420 


429 


439 


448 


457 


467 


476 


485 '495 -504 -513 


22 


380 


389 


399 -408 


417 


427 


436 


445 


454 


464 


473 


482; -491 


501 -510 


23 


377 


387 


396 -405 


414 


423 


433 


442 


451 


460 


469 


479 -488 


497 -506 


24 


375 


384 


'393 '4 02 


411 


420 


429 


439 


448 


457 


466 


475 -484 '493 '52 


25 


372 


381 


390 1 -399 


408 


417 


426 


435 


444 


453 


462 


471 


480 -489 


498 


26 


369 


377 


386 -395 


404 


'4*3 


422 


'43 1 


440 


449 


458 


467 


476 


485 


494 


27 


365 


374 


383 '392 


401 


410 


419 


428 


437 


446 


454 


463 


472 


-481 


490 


28 


362 


371 


380 -388 


397 


406 


415 


424 


433 


441 


45 


459 


468 


477 


486 


29 


359 


367 


376 


385 


394 


402 


411 


420 


429 


437 


446 


455 


464 


472 


481 


30 


355 


364 


372 


381 


390 


398 


407 


416 


424 


433 


442 


'450 


459 


468 


476 


31 


'35 1 


360 


369 


377 


386 


394 


'43 


411 


420 


429 


437 


446 


454 


463 


471 


32 


348 


356 


365 


373 


382 


390 


3991 '47 


416 


424 


433 


441 -449 


458 


466 


33 


344 


352 


361 


369 


377 


386 


394 


'43 


411 


419 


428 


436 -444 


453 


461 


34 


340 


348 


356 


365 


373 


381 


390 


398 


-406 


415 


423 


43 1 '439 


-448 


456 


35 


336 


344 


352 


360 


369 


377 


385 


393 


401 


410 


418 


426 -434 


442 


45 1 


36 


332 


34 


348 


356 


364 


372 


380 


388 


396 


45 


413 


421] -429 


437 


445 


37 


327 


335 


343 




359 


367 


375 


383 


39i 


399 


407 


4*5 -423 


43 1 


439 


38 


323 


331 


339 


347 


355 


362 


37 


378 


386 


394 


402 


410 


418; -426 


433 


39 


319 


326 


334 


342 


350 


357 


365 


373 


381 


389 


396 


404 


412-420 


427 


40 


314 


322 


329 


337 


345 


352 


360 


368 


375 


383 


391 


398 


406! -414 


421 


41 


309 


317 


325 -332 


34 


347 


355 


362 -370 


377 


385 


392 


400 -408 


415 


42 


35 


312 


320 -327 


334 


342 


349 


357 -364 


372 


379 


386; -394! '4 01 


409 


43 


300 


37 


314 


322 


329 


336 


'344 


351! -358 


366 


373 -380 -388 -395 


402 


44 


295 


302 


309 


317 


324 


331 


338 


345 


352 


360 


367, '374 


381 -388 


396 


45 


290 


297 


304 


3" 


318 


325 '332 


339 -346 


354 


361-368 


375 


382 


389 


46 


285 


292 


299 


306 


313 


320 -326 


3331 '34 


347 


354J -361 


368 


375 


382 


47 


28c 


286 


293 


300 


307 


314 


321 


327 '334 


34 1 


348| -355 


361 


368| -375 


48 


274 


281 


288 


294 


301 


308 


314 


3 2i| -328 


335 


34 1 


348 


355 


361 


368 


49 


26g 


276 


282 


289 


295 


302 


308 


3*5 


321 


328 


335 


341 


348 


354 


-361 


5 


264 


270 


276 


283 


289 


296 


302 


.309 


315 


321 


-328 


334 


341 


347 


354 


5I 


25* 


264 


271 


277 


283 


289 


296 


302 


308 


315 


321 


327 '334 


34 


346 


52 


252 


259 


265 


271 


277 


283! -289 


296 


302 


308 


314 -320! -326 


332 


339 


53 


247 


253 


259 


265 


271 


277 


283 


289! -295 


301 


307 -313 


319 


325 


331 


54 


241 


247 


253 


259 


265 


2 7 C 


276 


282 -288 


294 


300 -306 


312 


317 


323 


55 


23 = 


241 


247 


252 


258 


264 


270 


275 -281 


287 


293 -298 


34 


310 


315 


56 


22C 


235 


240 


246 


252 


257 -263 


268 


274 


280 


285 -291 


296 


302 


308 


57 


'22^ 


229 -234 


240 


245 


251 -256 


261 -267 


272 


278 -283 


289 


294 


300 


58 


217 


223 


228 


233 


.-238 


244 -249 


254 


260 


265 


270 -276 


281 


286 


291 


59 


211 


216 


221 


227 


232 


237 -242 


247 


252 


258 


263 -268 


273 


278 


283 


60 


205 


210 


215 


220 


225 


230 -235 


240 -245 


250 


255 -260 


265 


270 


275 


61 


195 


204 


208 


213 


218 


223 -228 


233 -238 


242 


247! -252 


257 


262 


267 


62 


192 


197 


2O2 


207 


211 


216 -221 


225 -230 


235 


239 -244 


249 


254 


258 


63 


186 


191 


195 


200 


20 4 


2O9 -213 


2l8j -222 


227 


232 -236 


241 


245 


250 


64 


i8c 


I8 4 


188 


193 


197 


202 -206 


210-215 


219 


224 


228 


232 


237 


241 


65 


173 


177 


182 


186 


I9O 


194 -199 


203' -207 


211 


216 


220 


224 


228 


232 






K 






' ' I 











61 
Traverse Table. 

SHOWING DIFFERENCE OF LONGITUDE AND CORRESPONDING DEPARTURE. 



ed 


DIFFERENCE OF LONGITUDE. 


58 


57 


58 


59 


60 


61 -62 


63 ! -64 


65 


66 


67 


68 


69 


70 
















I 




o 






















2 


560 -570; -580! -590 -600 


610 -620 -630 -640 -650 


660 


670 


680 


690 -7OO 


4 


559 -569 "579 -589 '599 


609 -618; -628 -638' -648 


658 


668 


678 


688 


698 


6 
8 

10 


557i -567 '577 -587 
555 -564 '574! -584 
551 -561 -571 -581 


|'597 
1-594 
591 


607 -017 -6271 -636 -646 
604 -614 -624' -634 -644 
6oii -611 -620 -630 -640 


656 

654 

650 


666 
663 
660 


676 

673 
670 


686 
683 
680 


696 

693 
689 


ii 


550 -560 -569 -579 -589 


599 -609 -618 -628 -638 


648 


658 


668 


677 


687 


12 


548 


558 -567 -577J -587 


597 


606 -616! -626 


636 


646 


655 


665 


675 


/ 

685 


13 


546 


555 


565| -575 -585 


594 


604; -614 -624 


633 


643 


653 


663 


672 


682 


14 


543 


553 


563; '572| -582 


592 


602 


611! -621 


631 


640 


650 


660 


670 


679 


15 


'54 1 


551 


560 -570 -580 


589 


599 -609 -618 -628 


638 


647 


657 


666 


676 


16 


538 


548 


558 -567-577 


586 


596 -606 -615! -625 


634-644 


654 


663 


673 


17 


536 


545 


555 -564 '574 


583 '593 


1 -602 -612 -622 


631 -641 


650 


660 


669 


18 


533 


542 


552! -561 -571 


580 


590 -599 -609 -618 


628 


637 


647 


656 


666 


19 


529 


539 


548 -558 -567 


577 


586; -596 -605 -615 


624 


633 


643 


652 


662 


20 


526 -536 -545 -554 -564 


573 


583 


592 -601 


611 


620 


630 


639 


648 


658 


21 


523! '532 


541 -551 -560 


569 


579 -588 -597 -607 


616 


625 


635 


644 


654 


22 


519 


528 


'538| -547 -556 


566 


575 


584 -593 -603 


612 


621 


630 


640 


649 


23 


515 


525 


534 "543 -552 


562 


571 


580 


589 -598 


608 


617 


626 


635 


644 


24 


512 


521 


530 -539 -548 


557 


566; -576 


585 '594 


603 


612 


621 


630 


639 


25 


508 


517 


526! -535 -544 


553 


562 


571 


58o 


589 


598 


607 


616 


625 


634 


26 


53 


512 -521 


530 


539 


548 -557 


1 -566 -575 


584 


593 


602 


611 


620 -629 


27 
28 

29 


499 
494 
490 


508-517 -526 
503 -512 521 
499i'57 -516 


535 
53 
525 


544 
539 
534 


552! -561 -570 
547| -556 -565 
542: -551 -560 


579 
574 
569 


588 
583 

577 


597 
592 
586 


606 
600 
595 


615; -624 
609 -618 
603! -612 


3 


485 


494 


502 


'5 1 * 


520 


528 -537 


546 -554 


563 


572 


580; -589 


598 -606 


31 


480 


489 


497 -506 


.514 


523 -531 '54 


549 


557 


566 -574 


583 


591 


600 


32 


475 


483 


492 -500 


59 


517 -526] -534 


543 


55i 


560 -568 


577 


585 


594 


33 


470 


478 -486 


495 


53 


512 -520 


I -528 -537 


545 


554 -562 


570 


579 


587 


34 


464 


473 


481 -489 


497 


506 -514 


522 -531 


539 


547 


555 


564 


572 


580 


35 


459 


467 


475 -483 


491 


500 -508 


516 


524 


532 


541 


549 -557 


565 


573 


36 


453 


461 


469 -477 


485 


494! -502 


510 


518 


526 


534 


542 -550 


558 -566 


37 


447 


455 


463 -471 


479 


487 '495 


503 


511 


519 


527 


535 -543 


551 


559 


38 


441 


'449 '457['465 


473 


481 -489 


496 


504 


512 


520 


528 -536 


544 -552 


39 


435 


443 


451' '459 


466 


474 -482 


490 


497 


55 


513 


521 


528 


536 -544 


40 


429 


437 -444 


452 


460 


467 -475 


483 


490 


498 


506 -513 


521 


529 -536 


41 


423 


43 '43 8 J '445 


'453 


460: -468 


475 


483 


491 


4981 -506 -513 


521! -528 


42 


416 


424] -431! .438 


446 


453J-46I 


468 


476 


483 


490 -498 -505 


513 


520 


43 


410 


417 -424! -431 


439 


446 -453 


'461 


468 -475 


483 


490! -497 


505 


512 


44 


43 


410! .417! -424 


432 


"439 '446 


453 


460 -468 


475 


482 -489 


496 


504 


45 


396 


403 


-410 


417 


424 


431 -438 


445 


453 -460 


-467 


474 


481 


488 


495 


46 


389 


396 


403 


410 


417 


424 '43ii -438 


445! -452 


458 


4 6 5 


472 


479 


486 


47 


382 


389 


396 


402 


409 


416 -423 


43 


436 1 -443 


450 


457 


464 




477 


48 


375 


381! -388 


395 


401 


4 o8|. 4 i5 


422 


428 -435 


442 


448 


455 


462 


468 


49 


367) '374 


381 


387 


394 


400 .4071 -413 


420; -426 


433 


440 


446 


453 


459 


5 


360 


366 


373 


379 


386 


392 -399 -45 


411 -418 


424 




437 


444 


450 


51 


352 


359 


365 


371 


378 


384 -390 


396 


403! -409 


415 


422J -428 


434 


441 


52 


345 


351 


357 


363 


369 


376 -382 


388 


394 -400 


406 


412-419 


425 


431 


53 


337 


343 


349 


355 


361 


367 '373 


379 


385 -391 


397 


403 -409 


415 


421 


54 


329 


335 


341 


347 


353 


359 -364 


370 


376 -382 


388 


394 -400 -406 -411 


55 


321 


327 


333 


338 


344 


350 -356 


361 


367 


373 


379 


384 -390 -3961 -402 


56 


3I3-3I9 


324 


33 


336 


34 1 


347 


352 


358 


363 


369 


375 


380 -386 


39i 


57 


3051-310 


316 


321 


327 


332 


338 


343 


349 -354 


359 


365 -370J -376 -381 


58 


297 


302; -307 


313 


318 


323 


329 


334 


339 -344 


350 


355 


360 -366 -371 


59 


288 


294 


299 -304 


309 


314 


319 


324 


33 '335 


34 


345 


350 -355 


361 


60 


280 


a8 5 


290 


295 


300 


305 


310 


315 


320 -325 


33 


335 


340 -345 


350 


61 


271 


276 -28l 


286 


291 


296 


301 


305 


31 -315 


320 


325 


33 -335 


339 


62 


263 


268 


272 


277 


282 


286 


291 


296 


300 -305 


310 


315 


3I9-324 


329 


63 


254 


259 


263 


268 


272 


277 


281 


286 


291 -295 


300 


304 


309 -313 


318 


64 


245 


250 


254 


259 


263 


267 


272 


276 


281 -285 


289 


294 


298 -302 


37 


65 


237 -241 


245 


249 


254 


258 -262 


266 


270 -275 


279 


283 


287 


292 


296 



62 

Traverse Table. 
SHOWING DIFFERENCE OF LONGITUDE AND CORRESPONDING DEPARTURE. 





DIFFERENCE 


OF LONGITUDE. 


3 




















71 -72 


73 


74 -75 


76 


77 


78 


79 -80 


81 -82 -83 -84 -85 


o 

2 


710 -720 


730 


740 -750 


76o| 


.770 


780 


790 -800 


810 -819 


829 -839 -849 


4 


708 


718 


728 


738 


748 


758 


768 


778' 


788 -798 


-808 -818 


828! -838 -848 


6 


706 


716 


726 


736 


746 


756! 


766 


776 


786 -796 


806 -816 


825 -835 -845 


8 


703 


713 


723 


733 


743 


753i 


763 


.772 


782 -792 


802! -812 


822 -832, -842 


10 


699 


709 


719 


729 


739 


748 


758 


768 


778 


788 


798 -808 


817 -827 -837 


ii 


697 


707 


717 


726 


736 


746 


756 


766 


775 -785 


795 '805 


815 -825! -834 


12 


694 


704 


714 


724 


734 


743 


753 


763 


773 


783 


792 -802 


812 -822 -831 


13 


692 


702 


711 


721 


731 


741 


750 


760 


770 


779 


789 -799 -809 -818 -828 


14 


689 


699 


708 


718 


728 


737 


747 '757 


767 


776 


786 -796 -805: -815! -825 


15 


686 


695 


75 


715 


:724 


734 


744 '753 


763 '773 


782 -792 


802 


811 -821 


16 


682 


692 


702 


711 


721 


731 


740 


75 


759 -769 


779 -788 


798 


807 -817 


17 


679 


689 


698 


708 


717 


727 


736 


746 


755 -765 


775 -784 


794 


803 -813 


18 


675 


685 


694 


704 


713 


723 


732 


742 


751 -761 


770 -780 


789 


799' -808 


19 


671 


681 


690 


700 


79 


719 


728 




747 


756 


766 -775 


785 


794 '804 


20 


667 


677 


686 


695 


705 


714 


724 


733 


742 


752 


761 


771 


780 


789; '799 


21 


663 


^672 


682 


691 


700 


710 


719 


728 


738 


'747 


756 


766 


775 


784; '794 


22 


658 


668 


677 


686 


695 


75 


714 


723 


732 


742 




760 


770 


779 -788 


23 


654 


663 


672 


681 


690 


700 


709 


718 


727 


736 


746 


755 


764 


773 -782 


24 


6 4 9 


658 


667 


676 


685 


694 


703 


713 


722 




74 


749 


758 


767 -777 


25 


643 


653 


662 


671 


680 


689 


698 


707 


716 -725 


734 


743 


752) -761 -770 


26 


638 


647 


656 


665 


674 


683 


692' -701 


710 -719 


728 


737 


746 '755 -764 


27 


633 


642 


650 


659 


668 


677 


686 -695 


74 


713 


722 


73 1 


740 -748; -757 


28 


627 


636 


645 


653 


662 


671 


680 -689 


698 


706 


715 


724 


7331 '742; -751 


29 


621 


630 


638 


647 


656 


665 


673 -682 


691 


700 


708 


717 


726 -735! -743 


30 


615 


624 


632 


641 


650 


658 


667 


675 


684 


693 


701 


710 


719! -727 -736 


3 1 


609 


617 


626 


634 


643 


651 


660 -669 -677 


686 


694 


703 


711 -720 -729 


3 2 


602 


611 


619 


628 


636 


645 


653 -661 


670 


678 


687 


695 


704: -712 -721 


33 


595 


604 


612 


621 


629 


637 


646 


654 


663 


671 


679 


688 


696 -704 -713 


34 


589 -597 


605 


613 


622 


630 


638 


647 


655 


663 


672 


680 


688 -696 -705 


35 


582 


590 


598 


606 


614 


623 


631 


639 


647 


655 


664 


672 


680 -688 -696 


36 


574 


582 


591 


599 


607 


615 


623 


631 


639 


647 


655 


663 


671 


680 -688 


37 


567 


575 


583 


59i 


599 


607 


615 


623 


631 


639 


647 


655 


663 


671 -679 


38 


559 


567 


575 


583 


591 


599 


607 


615 


623 


630 


638 


646 


654 


662 -670 


39 


552 


560 


567 


575 


583 


59i 


598 


606 


614 


622 


629 


637 


645 


653 -661 


40 


544 


552 


559 


567 


575 


'582 


590 -598 


605 


613 


620 


628 


636 


643 -651 


4 1 


536 


543 


'55 1 


558 


566 


574 


581 -589 


596 


604 


611 


619 


626 


634 '642 


42 


528 


535 


542 


55 


557 


565 


572 -580 




595 


602 


609 -617 


624 -632 


43 


519 


527 '534 


54 1 '549 


556 


563 -570 


578 


585 


592 -600 -607 


614 -622 


44 




5181-525 


532 -54 


547 


554 -561 


568 


575 


583 '590 


597 


604 


611 


45 


502 


509 -516 


523 -530 


537 


544 '552 


559 


566 


573 -580 


587 


594 


601 


46 

47 


493 -50 -57 
484 -491 -498 


514 -521 
'55! '5 11 


528 
518 


535 
525 


542 
532 


549 

539 


556 
546 


. -563-570 

552J -559 


577 -584 
566 -573 


590 
580 


48 


475 


482 -488 


495 -502 


59 


515 


522 


529 


535 


542 -549 


555 


562 


569 


49 


466 


472 '479 


485 '492 


'499 


505 


512 


518 


525 


531 


538 


545 


551 


558 


50 


456 


463 


469 


476 -482 


489 


495 


501 


508 


5M 


521 -527 


534 


54 


546 


5 i 


447 


453 


459 


466| -472 


478 


485 -491 


497 


53 


5io|- 5 i6 


522 


529 


535 


52 


437 


443 


449 


456; -462 


468 


474 


480 


486 


493 


499) -505 


511 


517 


523 


53 


427 


433 


439 


445J -451 


457 


463 


469 


475 


481 


487 


493 


500 


506 


512 


54 


417 


423 -429 


435! '44 1 


447 


453 


458 


464 


470 


476 


482 


4 88j -494 


500 


55 


407 


413 -419 


424 -430 


436 


442 


447 


453 


459 


465 


470 


476 


482 


488 


56 


397 


403 -408 


414 


419 


425 -431 


436 


442 


447 


'453 


459 


464 


470 


475 


57 


387 


392 -398 


'43 


408 


414 


419 


425 


430 


436 


441 


'447 


452 


457 


463 


58 


376 


382 -387 


392 


397 


'43 


408 


413 


419 


424 


429 


435 


44 


445 


45 


59 


366 


37 1 :-376 


38i 


386 


391 


397 


402 


407 


412 


417 


422 


427 


433 


438 


60 


355 


360 


365 


37 


375 


380 


385 '390 


395 


400 


45 


410 


4*5 


420 


425 


61 


344 


349 


354 


359 


364 


368 


373 -378 


383 


388 


393 


398 


402 


407 


412 


62 


333 


338 


343 


347 


352 


357 


361 -366 


371 


376 


380 


385 


390 


394 


399 


63 


322 


327 


331 


336 


34 


345 


350 '354 


359 


363 


368 


372 


377 


381 


386 


64 




316 


320 


324 


329 


333 


338 -342 


346 


351 


355 


359 


364 


368 


373 


65 


.300 


304 -309 


313 


317 


321 


325 


330 


334 


338 


342 '347 


351 


355 


359 



63 
Traverse Table. 

SHOWING DIFFERENCE OF LONGITUDE AND CORRESPONDING DEPARTURE. 



3 


86 -87 -88 




D 
89 


IFFERENCE 


OF 
92 


LONGITUDE. 


96 -97 -98 


99 1-00 


90 


91 I 


93 


i 
94 -95 


















I 




o 

2 


859 -809 


879 




889 -899 


909 


919 


929 939 -949 


959 -969 -979 


989 -999 


4 


858 -868 


8 7 8 




888 -898 


908 


918 


928 -938 -948 


958! -968 -978' 


988 


998 


6 


8551 '865 


875 




885 -895 


905 


915 


925 '935 '945 


955, -965 -975 


985 


995 


8 


852 -862 


8 7 i| 


8811-891 


901 


911 


921 -931! -941 


951 -96i -97 


980' -990 


10 


847 


857 


86 7 : 


876 


886 


896 


906 


916 -926 -936 


945 '955 -965 


975J -985 


ii 


844 


854 


864' 


874 


883 


893 


903 


913 -923 


933 


942 -952 -962 


972 -982 


12 


841 


851 


861 




871 


880 


890 


900 


910 -919 


929 


939 '949 -959 


968 


978 


13 


838 


848 


857 




867 


877 


887 


896 -906 -916 


926 


935 '945 '955 


965 


974 


14 


834 


844 


854' 


864 


873 


883 


893 -902 -912 


922 


931 -941 -951 


961 


97 


15 


831 


840 


850' 


860 


869 


879 


889 


898 -908 


918 


927 


937 '947 


956 


966 


16 


827 


836 


846 




856 -865 


875 


884 


894 


904 


913 


923 


932 -942 


952 


961 


17 


822 


832 


842 


851 -861 


870 


880 


889 -899 


908 


918 -928 -937 


947 


956 


18 


818 


827 


837 




846 


856 


865 


875 


884' -894 


904 


913! -923 -932 


942 


951 


19 


813 


823 


832 




842 


851 


860 


870 


879 -889 


898 


908 -917 -927 


936 


946 


20 


808 


818 


827 




836 


846 


855 


865 


874' '883 


893 


902 -912 -921 


93 


940 


21 


803 


812 


822 




831 


840 


850 


859 


868, -878 


887 


896 -906 -915 


924 


934 


22 


797 


807 


816 


825 


834 


844 


853 


862 -872 


881 


890 -899 -909 


918 


927 




792 


Soi -810 


819 


828 


838 


847 


856, -865 


874 


884 -893. -902 


911 


921 


24 


786 -79S 


804 




813 


822 


831 


840 


850 -859 


868 


877 -886 -895 


904 


914 


**| 

25 


779 


788 


798 


807 


816 


825! -834 


843 -852 


861 


870' -879 -888 1 


897 


906 


26 


'773 


782 


791 




800 -809 


818 


827 


836 


845 


854 


863 -872 -881 


890 


899 


27 


766 


'775 


7 8 4 i 


793 " 8 2 


8ni -820 


829 


838 


846 


855) -864 


873 


882 


891 


28 


'759 


768 


777 


786 -795 


803 


812 


821 


830 


839 


848 -856 -865^ 


874 


883 


29 
3 


752 -761 -770 
745 -753| -762 


778! -787 
771 -779 


796 

788 


805 
797 


813 
805 


822 
814 


831 
823 


840 -848 -857 
831 -840 -849 


866 
857 


875 
866 


3 1 
32 
33 
34 


737 
729 
721 
7*3 


746 
738 
73 
721 


754 
746; 
738 

73; 


763 -771 
755 -763 
746 '755 
738 -746 


780 
772 
763 
754 


789 
780 

772 
763 


797 
789 
780 

771 


806 

797 
788 

779 


814 
806 

797 

788 


823! -831 
814 -823 
805 -814 
796! -804 


840; 

831 
822 

8l2| 


8 4 9 
840 
830 

821 


857 
848 

839 
829 


35 


704 -713 


.721 


729 '737 


745 


754 


762 


.770 


778 


786 -795 


803 


811 


819 


36 


696 


704 


712 


720 


728 


736 


744 -752 


760 


769 


777 785 


793 


801 


809 


37 


687 


695 


703 


711 


719 


727 


735 


743 


751 


759 


767 '775 


783 


791 


799 


3 8 


678 


686 


693 


701 


709 


717 


725 


733 


741! -749 


756 


764 


772 


780 - 7 


39 


668 


676 


684" 


692 


699 


707 


715 


723 


73 1 


738 


746 


754 


762 


769 


777 


40 


659 


666 


674 


682 


689 


697 


75 


712 


720 


728 


735 


743 


75i 


758 


766 


41 


649 


*oS7 


664 


672 


679 


687 


694 


702 


709 -717 


725 


732 


74 


747 


755 


42 


639 


64? 


654 


661 


669 


676 


684 


691 


699; -706 


713 


721 


728 


736 


743 


43 


629' -636 


644 


651 


658 


666 


673 -680 


687 -695 


702 


79 


717 


724 


73 1 


44 


619 -626 


633 


640 -647 


655 


662 -669 


676 


683 


691 


698 


75 


712 


719 


T^ 

45 


608 -615 


622 


629 -636 


643 -651 


658 


665 


672 


679 


686 


693 


700 


707 


46 
47 
48 
49 
5 


597 '604 
587 '593 
575 -582 
564 -571 
553 '55? 


611 

600 
589 
577 
566 


618 -625 
607 -614 
596 -602 
584 -590 
572 '579 


632 
621 

597 

585 


639 
627 
616 
604 
59i 


646 

634 
622 
610 

598 


653 
641 
629 
617 
604 


660 
648 
636 
623 
611 


667 
655 
642 
630 
617 


674 
662 

649 
636 
624 


681 
668 
656 

643 
630 


688 

675 
662 
649 
636 


1-695 
682 
1-669 
656 
643 


52 

53 
54 
55 


541 '54* 
529 -53^ 
518 -524 

'55 '5 11 
493 -49? 


554 
542 
53 
517 
55 


56c 
54* 
53^ 
522 


566 
554 
> '542 
529 
> -516 


573 
5 6c 

54* 

X O C 

522 


575 

> -56e 

554 
541 
52* 


585 
573 
560 

547 
533 


592 
579 
566 

553 
539 


598 
585 
572 
558 
545 


604 
591 
578 
564 
551 


610 
597 

584 
57 
556 


617 
603 
590 
576 
562 


623 
6ic 

582 
56* 


629 
I -616 
>! -602 
588 
574 


56 

57 
5 8 


481 -48^ 
468 -47^ 
456 -461 


492 

479 
466 


49* 

48! 

472 


* '53 
490 

'477 


49^ 

.482 


> -514 
> -501 

488 


[ -520 
57 
> '493 


526 
512 
498 


53 1 
503 


537 
523 
509 


542 

528 

514 


548 
534 
519 


554 -559 
539 -545 
525J '53 


59 
60 


T~ -t 

443 '44* 
43 '43! 


453 
440 


45* 
44! 


J -464 
> -450 


4 6c 
45! 


> '474 '479 
, -460 -465 


484 
47 c 


.489 
475 


494 

480 


5o 
485 


505 
490 


495J -5 


61 
62 
63 
64 
65 


417 -422 
404 -40* 
390 -39! 
377 -38] 
363 -36* 


427 
4*3 
400 
386 
372 


43^ 
41* 
40, 

39< 


436 
5 -423 
I -409 
> '395 

y -380 


44: 

42; 
.4x2 

39< 

38' 


44 e 
7 -43^ 
\ -41* 
> -4: 
> '38* 


) -451 
' '437 
5 -422 

5 -40* 
) '393 


45^ 

441 
427 
412 
39/ 


461 
446 
431 
416 
401 


465 
451 
436 
421 
406 


470 
455 
440 
425 
410 


475 
460 

445 
43 
414 


4 8c 
46! 
44< 
43' 
4*1 


] -469 
> '454 
I -438 
* -423 




04 

Traverse Table. 

SHOWING DIFFERENCE OF LONGITUDE AND CORRESPONDING DEPARTURE. 



^J 


DIFFERENCE OF LONGITUDE. 


2 * 


10 


11 


12 


13 


14 


15 


16 -17 


18 


19 


20 


21 


22 


23 


24 


25 


o 






























65 


042 


04^ 


051 


55, '59 


06: 


$ -06* 


3 -07^ 


5 -07^ 


> -080 


08= 


o8c 


93 


09; 


IO] 


106 


66 


041 


<0 45 


o 4 c 


) -053 '57 


06] 


06, 


> -oQc 


) -07^ 


, -077 


081 




089 


09^ 


09* 


1 -102 


67 


035 


04' 


047 


' -051 -055 




> -06; 


5 -06C 


> -07C 


> -074 


078 -082 


086 




094 


L -098 


68 


037 


041 




049 -052 


o 5 e 


> -060 -06^ 


I -067 


r -071 


075 -o 7 c 


082 


o8( 


090 -094 


69 


o 3 e 


039 


42 


047 -050 




1- -57| >o61 


o6< 


068 


072 


75 


079 


o8s 


086 -090 


70 


34 


038 


041 


044^ -048 


051 


5. 


5 -05* 


062 


065 


06? 


072 


75 


070 


082 


086 


71 


033 


036 


035 


042 -046 


o 4 c 


055 


' -055 


05S 


O62 


065 


o6 


072 


07 c 


07? 


! -081 


72 


031 


034 


037 


040 -043 


046 


o 4 c 


> <0 53 


056 


059 


062 


065 


068 


071 


74 


[ -077 


73 


029 


032 


035 


038 -041 


04^ 


47 


' >O 5 C 


53 


056 


058 


061 


064 


067 


070 


> -073 


74 


028 


030 


33 


036 


039 


041 


044 -047 -050 


5 2 


055 


058 


061 


063 


066 


069 


75 


026 


028 


031 


034 


036 


039 


041 1 -044 


047 


4 9 


052 


54 


57 


o6c 


062 


065 


76 


024 


027 


029 


031 


034 


036 


039 -041 


044 


046 


048 


051 


53 


o 5 e 


058 


060 


77 


022 


025 


027 


029 


031 


034 


036 -038 


040 


043 


045 


047 


049 


052 


054 


056 


78 


021 


023 


025 


027 


029 


031 


33 


035 


037 


040 


042 


044 


046 


045 


050 -052 


79 


OI9 


O2I 


023 


025 


027 


029 


031 


032 


34 


036 


038 


040 


042 


44 


046! -048 


80 


017 


OI9 


O2I 


023 


024 


026 


028 


030 


031 


33 


35 


036 


038 


040 


042 -043 


81 


016 


017 


Oig 


020 


022 


023 


025 


027 


028 


030 


031 


033 


034 


036 


038' -039 


82 


OI 4 


OI 5 


OI 7 


018 


Oig 


021 


022 


024 


025 


026 


028 


029 


031 


032 


33 '35 


83 


012 


OI 3 


015 


016 


OI 7 


018 


019 


021 


022 


023 


024 


026 


027 


028 


029 -030 


84 


OIO 


oii| -013 


014 


OI 5 


016 


017 


018 


019 


020 


O2I 


022 


023 


024 


025: -026 
































l 


85 


OO9 


OIO 


OIO 


on 


012 


013 


OI 4 


015 


016 


OI 7 


017 


018 


019 


020 


O2I -O22 


86 


007 


008 


008 


009 


OIO 


OIO 


Oil 


012 -013 


OI 3 


014 


015 


015 


016 


017; -017 


87 


00 5 


006 


006 


007 


OO7 


008 


008 


OO9 -OO9 


OIO 


OIO 


Oil 


012 


OI2 


OI3 ! -013 


88 


003 


004 


004 


005 


005 


005 


O06 


OO6 -OO6 


007 


007 


007 


008 


008 


008 -009 


89 


OO2 


OO2 


OO2 


002 


OO2 


003 


003 


003 


003 


003 


003 


004 -004 


004 


004' -004 




DIFFERENCE OF LONGITUDE. 


+> 




3 






| 




1 
















25 


26 


27 


28 -29 


30 


31 


32 


33 -34 


35 


36 


37 -38 


39 


40 


o 


























65 


106 


no 


114 


118 -123 


127 


!3i -135 


139 -144 


148 


152 


156 -161 


165! -169 


66 


102 


106 


no 


114 -118 


122 


126 -130 


-I 34 -I 38 


142 


146 


150 -155 


159 -163 


67 


098 


IO2 


105 


109 -113 


117 


121 -125 


129 -133 


137 


1411 -145 -14^ 


152 


156 


68 


094 -097 


IOI 


105 -109 


112 


116 


120 


124 


127 




135 


139 -142 


1461 -150 


69 


090 


093 


097 


looj -104 


108 


III 


115 -118 


122 


125 


129 


133 -136 


140 -143 


70 


086 -089 


092 


096 -099 


103 


106 


109 


113 


116 


120 


123 


127 -130 


133 ' J 37 




081 -085 -088 


091 -094 


098 


IOI 


104 


107 


III 


114 


117 


120 -124 


127 


130 


72 


077 -080 -083 


087 -090 


093 


096 


099 


102 


I0 5 


108 


in 


114-117 


121 


124 


73 


073 -076 -079 


082 


08 5 


088 


091 


094 


096 


099 


102 


105 


108 -in 


114 


117 


74 


069 -072 -074 


077 -080 


083 


085 


088 


091 


094 


096 


099 


102 -105 


107 


IIO 


75 


065 -067, -070 


072; -075 


078 


080 


083 


085 


088 


091 


093 


096 -098 


IOI 


104 


76 


060 -063 -065 


068 -070 


073 


75 


77 


080 


082 


085 


087 


090 -092 


094 


097 


77 


057 -058 -061 


063, -065 


067 


070 


072 


074 


076 


079 


081 


083! -085 


088 


090 


78 


052! -054 -056 


058 -060 


062 


064 


067 


069 


071 


073 


75 


077 -079 


081 


083 


79 


048 -050 -052 


053 '55 


057 


059 


061 


06 3 


06 5 


067 


069 


071 -073 


074 


076 


80 


043 -045 -047 


049 


050 


052 


054 


056 


057 


059 


061 


063 


064 -066 


068 


069 


81 


039, -041 1 -042 


044 -045 


047 


048 


050 


052 


53 


55 


056 


058 -059 


061 


063 


82 


35 -036 -038 


039 -040 


042 


043 


45 


046 


047 


049 


050 


051 


053 


54 


056 


83 


030 


032 -033 


34 '35 


37 


038 


039 


040 


041 


043 


044 


045 -046 


048 


049 


84 


026 


027 -028 


029 -030 


031 


032 


033 


34 


036 


037 


038 -039 -040 


041 


042 


85 


022 


023 


024 


024 


02 5 


026 


027 


028 


029 


030 


3 i 


031 ,-032 -033 


034 


35 


86 


017 


018 


019 


020 


O2O 


021 


022 


022 


023 


024 


024 


025 -026 -027 


027 


028 


87 


013 


014 


014 


OI 5 


015 


016 


016 


017 


017 


018 


018 


019 -019 -020 


020 


021 


88 


009 


009 


009 


OIO 


OIO 


OIO 


Oil 


Oil 


012 


012 


012 


013, -013 -013 


014 


014 


89 


004 


005 


005 


005 


005 


005 


00 5 


006 -006 


OO6 


006 


006 -006 -007 


007 


007 














m 


1 







65 

Traverse Table. 
SHOWING DIFFERENCE OF LONGITUDE AND CORRESPONDING DEPARTURE. 



^J 


DIFFERENCE OF 


LONGITUDE. 




40 


41 


42 


43 


44 


45 


46 


47 


43 | 


49 


50 


51 -52 


53 


54 


55 


65 


169 


173 


177 


182 


186 


190 


194 


-199 


203 


207 


211 


2l6, -22Oj -224 


228 


232 


66 


163 -167 


171 


175 


179 


183 


187 


191 


195 


199 


203 


207 -212 -2l6 


220 


224 


67 


156 -160 -164 


168 


172 


176; 


180 


184 


188: 


191 


195 


199 -203 -207 


211 


215 


68 


150 -1541-157 


161 -165 


169) 


-172 


176 


180 


184 


I8 7 


191! -195 -199, '2O2 


206 


69 


143 


147 


151 


1541-158 


161 


165 -168, 


172 


176 


I 7 9 


183 -186 -190-194 


197 


70 


137 


140 


144 


i47J-i 5 o 


154 


157 -161 


164 


168 


171 


I 74 -I 7 8 


181 -185 


188 


71 


130 


133 


137 


140 -143 


147 


15 -153! 


156 


160 


163 


166 -169 


173 -176 


179 


72 


124 


127 


130 


133 -136 


139 


142 -145 


-148 


151 


155 


158 


1611 -164 -167 


170 


73 


117 


I2O 


123 


126 -129 


132 


134 -137! 


140 


143 


I 4 6 


149 


152 -155 -158 


161 


74 


IIO 


113 


116 


119 -121 


124 


127-136 


132 


135 


I 3 8 


141 


H3 


146 -149 


152 






















i 




75 


104 -106 


109 


III -114 


116 


119 -122 


124 


127 


129 


J 32 -135 -137 -140 


142 


76 


097 -099 


102 


104! -106 


109 


III 


114 


116 


119 


121 


123 -126 


128 -131 


133 


77 


090 -092 


-094 


0971 -099 


IOI 


103 


106 


108 


IIO 


112 


115 


117 


119 -121 


124 


78 
79 


083 
-076 


08 5 

078 


087 
080 


089 
082 


09! 

084 


094 

086 


096 
088 


098 
090 


100 

092 


102 

193 


104 -106! -108 
095! -097J -099 


IIO -112 
IOI -I0 3 


114 
105 


80 


069 -071 


073 


075 -076 


-078 


o8oj -082 


-083 


-085 


087 


089, -090 


092 -094 


096 


81 


063 -064 


066 


067 -069 


070 


072) -074 


075 


077 


078 -080! -081 


083 -084 


086 


82 


056 -057 


058 


060 


061 


063 


064 -065 


067 


-068 


070 


071 -072 


074 -075 


077 


83 


049 -050 


051 


052 


054 


055J 


056 -057 


058 


060 


061 


062 -063 -065 -066 


067 


84 


042 -043 


044 


045 -046 


47j 


048; -049 


050 


051 


052 


053 -54 -055 -056 


57 


85 


35 


036 


037 


037 


038 


039 


040 -041 


-042 


43 


044 


044 


045 -046 -047 


048 


86 


028 -029 


029 


030 


031 


031 


032 -033 


033 


34 


035 


036 -036! -037 -03? 


038 


87 


O2I -O2I 


022 


023 


023 


024 


024 -025 


-025 


026 


026 


027 -027 -028 -028 


029 


88 


OI 4 


OI 4 


OI 5 


015 


015 


016 


016 -016 


017 


017 


017 


018 -018 


018 -019 


019 


89 


-007 


007 


007 


008 


008 


008 


008 -008 


008 


009 


009 


009 -009 


009 -009 


OIO 










1 






















H~* 


DIFFERENCE OF 


LONGITUDE 





-55 


56 -57 


58 


58 


60 


61 


62 


63 


64 


65 


66 


67 


58 


69 


70 


65 


232 -237 


2 4 I 


245 


249 


254 


258 


262! -266 


270 


275 


279 


283 


287 


292 


296 


66 


224 


228 -232 


236 


240 


244 


248 


252 


256 


260 


264 


268 


273 


277 


281 


285 


67 


215 


219 -223 


227 


231 


234 


-238 


242 


246 


250 


254J -258 


262 


266 


270 -274 


68 


206 


210 -214 


217 


221 


225 


229 


232 


236 


240 


243 


247 


251 


255 


258] -262 


69 


197 


201 


-204 


208 


211 


215 


219 


222 


226 


229 


233 


237 


240 


244 


247 -251 
































7 


188 


192 -195 


198 


2O2 


205 


209 


212 


215 


219 


222 


226 


229! -233 


236 -239 


7 1 


179 


182 -186 


189 


192 


195 


199 


2O2 


205 


208 


212 


215 


218 


221 


225 


228 


72 


170 


173-176 


179 


182 


185 


189 


I92I-I95 


198 


2OI 


204 


207 


2IO 


213 


216 


73 


161 


164 -167 


170 


172 


175 


178 


181 


184 


187 


I9O 


193 


196 


199 


202J -205 


74 


152 


I54-I57 


160 


I6 3 


165 


168 


171 -174 


176 


179 


182 


185 


I8 7 


190 


193 


75 


142 


145 -148 


150 


153 


155 


158 


160 


163 


166 


168 


171 


173 


I 7 6 


179 


181 


76 


133 


135 -138 


140 -143 


145 


148 


150; -152 


155 


157! -160 


162 


165 


I6 7 


169 


77 


124 


126; -128 


130 


133 


135 


137 


139 


142 


144 


146 -148 


151 


153 


155 


157 


78 


114 


116 -119 -I2i -123 


125 


127 


129 


-131 


133 


.-135 -137 


139 


141 


143 


146 


79 


105 


107 


109 -III -113 


114 


116 


118 


120 


122 


124 


126 


128 


130 


I 3 2 


134 


80 


096 


09? 


099 -101 


IO2 


104 


106 


io8j -109 


III 


113 


J.II5 


116 


118 


120 


122 


81 


086 


088 -089 -091 


O92 


094 


095 


097 


099 


IOO 


IO2 


-103 


105 


106 


108 


IIO 


82 


077 


078 -079 -081 


082 


084! -085 


086 


088 


089 


090 -092 -093 -095 


096 


097 


83 


067 -068, -069 -071 


072 


73 


074 


076 


077 -078 


079 


080 -082! -083 


084 


085 


84 


57 


059 -060 


061 -062 


063! -064 


065 


066: -067 


068 


069 -070 


071 


072 


073 


85 


048 -040 


I -050 


051 


5 I 


052 


53 


54 


055 


056 


057 


058 -058 


059 


060 


161 


86 


038 


039 -040; -040 


4 I 


042 


043 


043 


44 


045 


045 


0461 -047 -047 


048 


049 


87 


029 -029 -030 -030 


3 I 


031 


032 


032 


033 


33 


034 


035 >0 35 


036 


036 


037 


88 


OI9 -O2O -O2OJ -O20 


021 


021 


021 


022 


O22 


022 


023 


-023 -023 -024 


024 


024 


89 


OIO -OIO -OIO -OIO 


OIO 


OIO 


Oil 


Oil 


Oil 


Oil 


Oil 


OI2i -012 -OI2 

1 i 


012 -OI2 




















1 





5 Azimuth. 



66 

Traverse Table. 

SHOWING DIFFERENCE OF LONGITUDE AND CORRESPONDING DEPARTURE. 





DIFFERENCE OF LONGITUDE. 


3 

































70 


71 


72 


73 


74 


75 


76 


77 


78 1 79 


80 


81 


82 


83 


84 


85 


o 


















i : ' I ! 


65 


296 


300 


304 


309 


313 


3i7 


321 


325 -330 -334 


338 


342 -347 -351 -355 -359 


66 


285 


289 


293 


297 


301 


35 


39 


3 J 3 '3 I 7 -321 


325 


329 -334 -338 -342 -346 


67 


274 


277 


281 


285 


289 


293 


297 


301 


305 -309 


313 


316 -320 -324 -328, -332 


68 


262 


266 


270 


273 


277 


281 


285 


288 


292! -296 


300 


33 


37 


3ii 


315 


318 


; 69 


251 


254 


258 


262 


265 


269 


272 


276 -28c 


283 


.28 7 


290 


294 


297 


301 


35 


70 


239 


243 


246 


250 


253 


257 


260 


263 


267 


270 


274 


277 


280 


284 -287 


291 


7* 


228 


231 


234 


238 


241 


' 2 44 


247 


251 


254 


257 


260 


264 -267 


270 -273 -277 


72 


216 


219 


222 


226 


229 


232 


235 


238 


241 


244 


247 


250 -253 -256 -260! -263 


73 


205 


208 


211 


213 


216 


219 


222 


225 


228 


231 


234 


237 -240 -243 -2 4 e 


249 


74 


193 


196 


I 9 8 


201 


204 


207 


209 


212 


215 


218 


221 


223! -226 


229 


232 


234 


75 


181 


184 


186 


I8 9 


192 


194 


197 


199 


202 


204 


20 7 


2IOJ -212 


215 


217 


220 


76 


169 


172 


174 


177 


179 


181 


I8 4 


186' -i8g 


191 


194 


196 -198 


2OI 


203 


206 


77 


157 


160 


162 


I6 4 


166 


169 


171 


I 73|-i75 


178 


180 


182 -184, -187 


i8g 


191 


78 


146 


148 


150 


152 


154 


156 


158 


160 -162 


164 


166 


168 -170 


-I 73 -175 


177 


79 


134 


135 


137 


139 


141 


*43 


!45 


147 -149 


^I 


153 


J 55 


156 


158 -i6c 


162 


80 


122 


123 


125 


127 


128 


130 


132 


134 


135 


137 


139 


141 


142 


144 -146 


148 


81 


no 


in 


113 


II 4 


116 


117 


119 


120 -122 


124 


125 


127 


128 


130: -131 


133 


82 


097 


099 


100 


IO2 


103 


104 


106 


107 -109 


no 


in 


II3J-II4 


116' -117 


118 


83 


085 


087 


088 


089 


090 


091 


093 


094 '095 


096 


097 


099 -ioo 


IOI -IO2 


104 


84 


073 


074 


075 


076 


077 


078 


079 


080 -082 


083 


084' -085 


086 


087' -088 


089 


85 


061 


062 


063 


064 


064 


065 


066 


067 -O68 


069 


070 


071 -071 


072 


073 


074 


86 


049 


050 


050 


5 I 


052 


052 


053 


054 


54 


55 


056 


057 -057 


058 


059 -059 


87 


037 


037 


038 


038 -039 


039 


040 -040 


4 I 


041 


042 


4 2 | -043 


43 


44 


044 


88 


024 


025 


025 


025 


026 


026 


027 -027 


027 


028 


028 


028 -029 


029 


029] -030 


89 


OI2 


012 


013 


013 


013 


013 


013 -013 


OI 4 


014 


014 


014 -014 -014 


0151-015 




DIFFERENCE OF LONGITUDE. 


3 










1 






1 






j 




85 


86 


87 


88 


89 


90 -91 


92 


93 -94 


95 


96 


97 -98 


99 1-00 


65 


359 


363 


368 


372 


376 


380 -385 


389 


393 


397 


401: -406 


410 -414 


418 -423 


66 


346 


350 


354 


358 


362 


366 -370 


374 


378, -382 


386 -390 


395 '399 


403! -407 


67 


332 -336 


34 


344 


348 


352 -356 


359 


363 -367 


37ii-375 


379, -383 


387 : -391 


68 


318 -322 


326 


330 


333 


337 -341 


345 


348, -352 


356. -360 


363' -367 


371-375 


69 


35 '38 -3 12 


315 


319 


323 -326-330 


333 


337 


34 '344 


348-35I 


355 


358 


70 


291 -294 


298 


301 


304 


308 -311 


315 


318 


321 


325 -328 


332 '335 


339 


342 


71 


277 -280 


283 


287 


290 


293 -296 


300 


33 


306 


39 -313 


316: -319 


322 


326 


72 


263! -266 


269 -272 


275 


278 -281 


284 


287 -290 


294 -297 


3, -303 


306 


309 


73 

74 


249 -251 
234 -237 


254 
240 


257 
243 


260 
245 


263! -266 
248; -251 


269 
254 


272 
256 


275 
259 


278 -281 
262 -265 


284 -287 
267 -270 


289 
273 


292 
276 


75 


220 


223 


225 


228 


230 


233-236 


238 


241 


243 


246 -248 


251 -254 


256 


259 


76 


206 -208 


2IO -213 


215 


2l8 -220 


223 


225 


227 


230 -232 


235 -237 


240 


242 


77 


191 -193 


196 -198 


200 


202 -205 


207 


209 


211 


214 -216 


2l8 -220 


223 


225 


78 


177 -179 -181] -183 


185 


187 -189 


191 


193 


195 


198 -200 


202 -204 


206 


208 


79 


162! -164 


166 


168 


170 


172 


174 


176 


177 


179 


181 -183 


185-187 


189 


191 


80 


148 -149 


151 


153 


155 


156 


158 


160 


161 


I6 3 


165-167 


168 -170 


172 


174 


Si 


133 


135 


136 


138 


139 


I 4 I 


142 


144 


145 


I 47 


149-150 


152-153 


155 


156 


82 


118 -120 


121 


122 


124 


125 -127 


128 


129 


131 


132 -134 


135 -136 


138 


139 


83 


104 -105 


106 


107 


108 


no -in 


112 


ii3 


115 


116 -117 


118 -119 


121 


122 


84 


089 -090 


091 


092 -093 


094 


095 


096 


097 


098 


099 -100 -101; -I02'-I03 


I0 5 


85 


074 


075 


076 


077 -078 


078 


079 


080 


081 


082 


083' -084 -085 -085 -086 


087 


86 


059 -060 -061 


061 -062 


063 


063 


064 


065 


066 


066 -067 -068 -068 -069 


070 


87 


044! -045: -046 -046 -047 


047 


048 


048 


049 


049 


050 -050 -051 -051 -052 


052 


88 


030 


030! -030 


031 -031 


031 


032 


3 2 


032 


033 


033 


034 -034. -034 -035 


035 


89 


015 -015! -015 


015! -016 


016 


016 


016 


016 


016 


017 -017 -017, -017 -017 


017 


' ! ! 








! ! 



Traverse Table. 
SHOWING DIFFERENCE OF LONGITUDE AND CORRESPONDING DEPARTURE. 





DIFFERENCE OF LONGITUDE. 


ta 














1-00 1-01 


1-02 1-03 


1-04 


1-05 


1-06 1-07 


1*08' 1-09 


1-10 Ml 


1-121 1-13 1-14 1-15 

I 


o 


























65 


423; -427, 


43 1 '435 


440 


444 


448 -452 


456 


4 6l 


465 -469 


473 


478 


4 82 -486 


66 


407: -411 


415 -419 -423 


427 


431 '435 


439 


443 


447 -451 


456 


460 


464' -468 


67 


39V395 


399 -402 -406 


410 


414 -418 


422 -426 


430 -434 


438 


442 


445 -449 


68 


375 -378, 


382, -386 -390 


393 


397 -401 


405! -408 


412 -416 


420! 


423 


427 '4.11 


69 


358 


362; 


366 -369 


373 


37 6 


380, -383 


387 


391 


394J -398 


401 1 


405 


409 


412 


70 


342 


345; 


349 -352 


356 


359^ 


363 -366I 


369 


373 


376 -380 


383 


386 


390 


393 


71 


326 


329; 


332; -335 


339 


342 


345 -348 


352 


355 


358| -361 


365 


368 


371 


374 


72 


309 


312 


3I5I-3I8 


321 


324 


328 -331 


334 '337 


34 '343 


346 


349 


352 


355 


73 


292 


295 


298 -301 


34 


307 


31, -313 


316 


319 


322J -325 




330 


"333 


336 


74 


276 


278 


28r -284 


287 


289 


292 -295 


298 


300 


33| -36 


309 




314 


317 


75 


259 


261 


264 -267 


269 


272 


274' -277 


280 


282 


285! -287 


1 
290 


292 


295 


298 


76 


242 


244 


247 -249 


252 


254 


256 -259 


261 


264 


266 -269 


271 


273 


276 


278 


77 


225 


227 


229 -232 


234 


236 


238 -241 


243 


245 


247 -250 


252' 


254 


256 


259 


78 


208 


210 


212 -214 


216 


218 


22O -222 


225 -227 


229 -231 


233 


235 


-2 3 7J -239 


79 


191 


193 


195-197 


198 


200 


2O2 -204 


206 -208 


210 -212 


214 


216 


218 -219 














1 










80 


174 


175 


I77-I79-I8I 


182 


184 -186 


188 -189 


191 -193 


194 


196 


igSJ -200 


81 


156 


158 


160 -161! -163 


164 


166; -1671 


169 -171 


172 -174 


175 


177 


178 -180 


82 


139 


141 


142 -143 


145 


146 


148-149) 


150 -152 


I53J-I54 


156 


157 


159 -160 


83 


122 


123 


124! -126 -127 


128 


129 -130) 


132 


133 


!34 -135 -136 


138 


139 -140 


84 


I0 5 


I 06 


107 -108! -109 


no 


III -112 


113 


114 


1151 -116 -117 


118 -119 -120 














i 










85 


087 


088 


089 


090 


091 


092 


092 -093 


094 -95 


096 


097 -098 


098 .099 


100 


86 


7 


070 


071 


072 


073 


073 


-074 -075 


075 -076 


077 


077 -078 


079 -080 


080 


87 


052 


053 


53 


054 


054 


055 


-055 -056 


057! -57 


058 


058 -059 


059 -060 


060 


88 


35 


035 


036 


036 


036 


037 


0371 '37 


038 -038 


038 


039 -039 


039 -040 


040 


89 


017 


018 


018 


018 


018 


018 


018 -019 


019 -019 


019 


019 -020 


020 -020 


020 


^j 


DIFFERENCE OF LONGITUDE. 


^ 


1-15 


1-16 



1-17 


1-18 1-19 


1-20 


1-21 


1-22 


1-23 1-24 


1-25 


1-26 


1-27 


1-28 


1-29 1*30 


o 

65 


486 


-490 


494 


499 


503 


507 


511 


516 


520 -524 


528 -532 


537 


541 


545J -549 


66 


468 


472 


476 


480 -484 


488 


492 


496 


500 -504 


508; -512 


517 




525| -529 


67 


449 


453 


457 


461 


465 


-469 


473 


477 -481 -485 


488 -492 


496; -500 


504! -508 


68 


43 1 


435 


438 


442J -446 


45 


453 


457 -461 -465 


468 -472 


476 


479 


483 -487 


69 


412 


416 


419 


4 2 3 ( -426 


43 


434 


437 


441 


444 


448 


452 


455 


459 


462 -466 
































7 


393 '397 


i -400 


404 -407 


410 


414 


417-421 


424 


428 


431 


434i -438 


'44 1 '445 


7 1 


374 


378 


381 


384 -387 


391 


394 


3971 -4 


404 


407 


410 -4131-417 


420 -423 


72 
73 


355 
336 


358 S -362 
339 -342 


365 -368 
345 -348 


371 '374 
351 '354 


377 -380 
357 -360 


383 
363 


386 
365 


389 
368 


392 -396 
37 I !'374 


399 
377 


402 
380 


74 


317 


-320 -322 


325 -328 


331 


334 


336 


339 


342 


345 


347 


35j '353 


356 


358 


75 


298 


3 -303! -305 '38 


. 3II 


313 


-316 


318 


321 


324 


326 


329 


33. 


334 


336 


76 


278 


281 


283 -285 -288 


290 


293 


295 


298 


300 


302 


305 


307 


310 


312 


314 




259 -261 
239 -241 


;-26 3 


265 -268 
245 -247 


270 -272 
249 -252 


274 
254 


277 
256 


279 
258 


281 
260 


283 
262 


286 -288 
264 -266 


290 
268 


292 
270 


79 


219 -221 


223 


225 -227 


229 -231 


233 


235 


237 


239 


240 


242 


244 


246 -248 


80 


200 -201 


; -203 


20 


; -207 


208, -2IO 


212 


214 


215 


217 


219 


221 


222 


224 -226 


81 


i8c 


181 


1-183 


i85 ! -i86 


i88 ! -189 


191 


192 


194 


196 


197 


199 


200 


2O2J -203 


82 


i6c 


161 


163 


164' -166 


167 -168 


170 -171 


173 


174 


175 


-177 


I 7 8 


180 -181 


83 


I4C 


141 


143 


144 -145 


146 -147 


149 


150 




152 


154 


155 


156 


157 -158 


84 


I2C 


121 


; -122 


123 -124 


125-126 


128 


129 


-130 


131 


-132 


133 


134.135 


130 


85 


IOC 


IOI -102 




i -104 


1051 -105 


106 


107 


108 


109 


no! -in 


II2J -112 


"3 


*y 

86 


o8c 


-081 -082 


082 -oS^i 


084^ -084 


085 


086 


086 


087 


-088 -089 


089 -090 -091 


87 


o6c 


> -061 -061 -062 -062 


063 -063 


064 


064 


065 


065 


-066 -066 


06 7 


o68j -068 


88 


040 


i -040 -041 


041 -042 


042 -042 


043 


043 


043 


044 


044 -044 


045 


045 -045 


89 


02C 


> -02C 


) -O2OJ -O2I -O2I 


021 


O2I 


021 


O2I 


022 


022 


022 -022 


022 


022. -023 



68 

Table C 1 . 
AZIMUTH CORRESPONDING TO A AND B CORRECTION IN DEPARTURE. 



A&B Az. 


A & H Ax. 


A & B Az. 


A A- n A/. 


A & B Az. 


A&B Az. 


A & B Az. 


/ 

ooo 90-0 


112 83-6 


227 77-2 


348 70-8 


479 64-4 


627 57-9 


798 51^4 


OO2 89-9 


114 "5 


229 -i 


35 '7 


481 -3 


630 


801 -3 


003 -8 


116 -4 


231 77-0 


352 -6 


483 -2 


632 -7 


804 -2 


005 -7 


ii/ '3 


23^ 7 6 '9 


354 70-5 


486 -i 


635 '6 


807 -i 


007 -6 


119 -2 


235 '8 


35t> -4 


488 64-0 


6 37 57-5 


810 51-0 


009 89-5 


121 -I 


236 -7 


358 -3 


490 63-9 


640 - 4 


813 50-9 


OIO -4 


123 83-0 


238 -6 


360 2 


492 -8 


642 -3 


816 -8 


OI2 -3 


125 82-9 


240 76-5 


362 -I 


'494 '7 


644 2 


818 -7 


014 -2 


126 -8 


242 -4 


364 70-0 


496 () 


647 -I 


821 -6 


016 -i 


128 -7 


244 "3 


366 69-9 


499 63-5 


649 57-0 


824 50-5 


017 89-0 


130 -6 


246 -2 


368 -8 


501 -4 


652 56-9 


827 -4 


019 88-9 


132 82-5 


248 -I 


37 '7 


503 '3 


654 -8 


830 -3 


021 -8 


133 '4 


249 76-0 


372 -6 


505 '2 


657 -7 


833 '2 


023 -7 


135 "3 


251 75-9 


374 r >9-5 


57 "I 


659 -6 


836 50-1 


024 -6 


137 -2 


253 


376 -4 


510 03-0 


662 56-5 


839 50-0 


026 88-5 


139 i 


255 "7 


37 8 '3 


512 62-9 


664 -4 


842 49-9 


028 -4 


141 82-0 


257 -6 


380 -2 


514 -8 


667 -3 


845 '8 


03 "3 


142 81-9 


259 75'5 


382 -I 


516 -7 


669 -2 


848 -7 


031 -2 


144 -8 


261 -4 


384 69-0 


518 -6 


672 -I 


851 -6 


33 "I 


146 -7 


262 -3 


386 68-9 


521 62-5 


674 56-0 


854 49-5 


035 88-0 


148 -6 


264 -2 


388 -8 


523 '4 


677 55-9 


857 -4 


037 87-9 


149 81-5 


266 -I 


390 -7 


525 '3 


680 -8 


860 -3 


038 -8 


151 '4 


268 75-0 


392 -6 


527 "2 


682 -7 


863 -2 


040 -7 


*53 "3 


270 74-9 


'394 68-5 


53 -i 


685 -6 


866 -i 


042 -6 


155 "2 


272 -8 


396 '4 


532 62-0 


687 55'5 


869 49-0 


044 87-5 


156 -i 


274 -7 


398 -3 


534 6l '9 


690 -4 


872 48-9 


45 "4 


158 81-0 


275 '6 


400 -2 


536 -8 


692 -3 


875 '8 


47 "3 


i 60 80-9 


277 74'5 


402 I 


538 -7 


695 -2 


878 .7 


049 -2 


162 -8 


279 -4 


404 68-0 


541 -6 


698 -i 


882 -6 


051 -i 


164 -7 


281 -3 


406 67-9 


543 61-5 


700 55-0 


885 48-5 


052 87-0 


166 -6 


283 -2 


408 -8 


545 '4 


703 54'9 


888 -4 


054 86-9 


167 80-5 


285 -i 


410 -7 


547 '3 


705 -8 


891 -3 


056 -8 


169 -4 


287 74-0 


412 6 


55 '2 


708 -7 


894 -2 


058 -7 


I7i "3 


289 73-9 


414 67-5 


552 -i 


711 -6 


897 -i 


059 -6 


173 -2 


290 -8 


416 -4 


554 61-0 


713 54'5 


900 48-0 


061 86-5 


175 -i 


292 -7 


418 -3 


'557 6o '9 


716 -4 


904 47-9 


063 -4 


176 80-0 


294 "6 


420 -2 


559 -8 


719 -3 


907 -8 


'5 '3 


178 79-9 


296 73-5 


4 22 -I 


561 -7 


721 -2 


910 -7 


066 -2 


180 -8 


298 -4 


424 67-0 


563 -6 


724 'I 


913 '6 


068 -i 


182 -7 


3 '3 


427 66-9 


566 60-5 


727 54' 


916 47-5 


070 86-0 


184 -6 


302 -2 


429 -8 


568 -4 


729 53'9 


919 '4 


072 85-9 


185 795 


304 -I 


43* '7 


57 "3 


732 -8 


923 -3 


073 -8 


187 -4 


306 73-0 


433 "6 


573 '2 


735 '7 


926 -2 


075 "7 


189 -3 


308 72-9 


'435 66 '5 


575 'I 


737 '6 


929 'I 


077 -6 


191 -2 


310 -8 


437 '4 


577 60-0 


74 53-5 


932 47-o 


079 85-5 


193 "I 


3ii -7 


439 -3 


580 59-9 


'743 '4 


936 46-9 


080 -4 


194 79-0 


313 "6 


441 -2 


582 -8 


745 '3 


939 -8 


082 -3 


196 78-9 


315 72-5 


443 'I 


584 -7 


74 8 -2 


942 -7 


08 4 -2 


198 -8 


317 "4 


445 66-0 


587 '6 


751 'I 


946 -6 


086 -I 


200 -7 


319 -3 


447 6 5'9 


589 59'5 


754 53-o 


949 46-5 


087 85-0 


202 -6 


321 -2 


449 


591 '4 


756 52-9 


952 -4 


089 84-9 


203 -5 


323 'I 


452 -7 


594 '3 


759 -8 


95" '3 


091 -8 


205 - 4 


325 72-0 


454 -o 


596 -2 


762 -7 


959 -2 


093 -7 


207 -3 


327 71-9 


456 ''.5-5 


598 -i 


765 -6 


962 -i 


095 -6 


2O9 -2 


329 -8 


458 -4 


601 59-0 


767 52-5 


966 46-0 


096 84-5 


211 -I 


33 1 "7 


460 -3 


603 58-9 


770 -4 


969 45'9 


098 -4 


213 78-0 


333 '6 


462 -2 


606 -8 


773 "3 


972 -8 


100 -3 


214 77-9 


335 7i-5 


464 -I 


6o,S -7 


776 -2 


976 -7 


IO2 -2 


216 -8 


336 -4 


466 65-0 


610 -6 


778 -I 


979 -6 


IO3 -I 


218 -7 


338' '3 


468 64-9 


613 58-5 


781 5 2-0 


983 45'5 


105 84-0 


220 -6 


340 -2 


471 -8 


615 -4 


784 51-9 


986 -4 


;I0 7 83-9 


222 77-5 


342 -i 


473 "7 


618 -3 


787 -8 


990 -3 


109 -8 


224 -4 


344 7i- 


475 "6 


620 -2 


790 -7 


993 '2 


no -7 


225 -3 


346 70-9 


477 6 4'5 


622 -I 


793 '6 


996 -i 


112 -6 


227 -2 


348 -8 


479 -4 


625 58-0 


'795 5 I- 5 


ooo 45-0 



69 

Table C 1 . 
AZIMUTH CORRESPONDING TO A AND B CORRECTION IN DEPARTURE. 



A & B Az. 


A & B Az. 


A&B Az. 


A & B Az. 


A&B Ax. 


A&B Az. 


A&B Az. 


/ / 

i-ooo 45 o 


I 'Q38 43 55 


1-078 42 51 


i -119 41 47 


/ o / 

1-162 40 43 


1-207 39 39 


1-253 38 35 


i -ooi 44 59 


i-39 54 


1-079 42 50 


1-120 46 


1-163 42 


1-207 38 


1-254 34 


I -001 58 


1-040 53 


1-079 49 


1-120 41 45 


1-163 4i 


1-208 37 


1-255 33 


1-002 57 


1-040 52 


1-080 48 


I-I2I 44 


1-164 4 4 


1-209 36 


1-256 32 


i -002 56 


1-041 5i 


i -080 47 


1-122 45 


l -i5 39 


1-209 39 35 


1-256 31 


i-o3 44 55 


1-042 43 50 


1-081 46 


I 122 42 


1-165 38 


1-210 34 


1-257 38 30 


1-003 54 


1-042 49 


1-082 42 45 


1-123 4 1 


1-166 37 


I -21 1 3 


1-258 29 


1-004 53 


1-043 48 


1-082 4<; 


1-124 4 1 4 


1-167 36 


1-212 32 


1-259 28 


1-005 52 


1-043 47 


I - 8 3 43 


1-124 39 


1-167 4 ^5 


I-2I2 31 


1-259 27 


1-005 51 


1-044 46 


1-084 42 


1-125 38 


1-168 34 


1-213 39 3 


1-260 26 


i -006 44 50 


1-045 43 45 


1-084 4 1 


1-120 37 


1-169 33 


1-214 29 


1-261 38 25 


i -006 49 


1-045 44 


1-085 42 40 


1-126 36 


1-169 32 


1-214 28 


1-262 ii 


1-007 48 


1-046 41 


i -086 39 


1-127 4 1 35 


1-170 31 


1-215 2 7 


1-262 2' 


i -008 47 


1-046 42 


1-086 38 


1-128 34 


1-171 40 30 


1-216 26 


I-263 22 


I -008 46 


1-047 41 


i 087 37 


1-128 33 


1-171 29 


1-217 39 25 


1-264 21 


1-009 44 45 


1-048 43 40 


1-087 36 


1-129 32 


1-172 28 


I-2I7 2" 


1-265 38 20 


1-009 44 


1-048 39 


i -088 42 35 


1-130 31 


1-173 27 


I-2I8 23 


1-265 Z 9 


i-oio 43 


1-049 38 


1-089 34 


1-130 41 30 


1-174 26 


I-2I9 22 


1-266 1 8 


i-oio 42 


1-049 37 


1-089 33 


1-131 29 


1-174 4 25 


1-220 21 


1-267 1 7 


i-on 41 


1-050 36 


1-090 32 


1-132 28 


1-175 24 


1-220 39 20 


1-268 16 


1-012 44 40 


1-051 43 35 


1-091 31 


1-132 27 


1-176 23 


I-22I 19 


1-268 38 15 


1-012 39 


1-051 34 


1-091 42 30 


1-133 26 


I-I76 22 


1-222 l8 


1-269 14 


1-013 38 


1-052 33 


1-092 29 


1-134 4 1 25 


I-I77 21 


1-222 17 


1-270 i' : 


1-013 37 


1-053 32 


1-093 28 


1-134 24 


1-178 40 2O 


1-223 J 6 


1-271 12 


1-014 36 


1-053 3i 


1-093 27 


I-I35 23 


I-I78 19 


1-224 39 I 5 


1-271 ii 


1-015 44 35 


1-054 43 3 


1-094 26 


1-136 22 


1-179 18 


1-225 I< 


1-272 38 10 


1-015 34 


1-054 29 


1-094 4 2 25 


I-I36 21 


1-180 17 


1-226 I; 


1-273 9 


1-016 33 


1-055 28 


1-095 24 


I-I37 4 I 20 


1-181 16 


1-226 12 


1-274 


1-016 32 


1-056 27 


1-096 23 


1-137 19 


1-181 40 15 


1-227 I][ 


1-275 7 


1-017 31 


1-056 26 


1-096 22 


1-138 18 


1-182 14 


1-228 39 10 


1-275 6 


1-018 44 30 


1-057 43 25 


1-097 21 


1-139 17 


1-183 13 


1-228 " 9 


1-276 38 5 


1-018 29 


1-057 24 


1-098 42 20 


1-140 16 


1-183 I2 


1-229 8 


1-277 4 


1-019 28 


1-058 23 


1-098 ig 


I-I 4 41 ! 5 


1-184 JI 


1-230 7 


1-278 3 


1-019 27 


I-O59 22 


i 099 18 


1-141 14 


1-185 4 I0 


1-230 6 


1-278 2 


I-O2O 20 


1-059 21 


i-ioo 17 


1-142 13 


1-185 9 


1-231 39 5 


1-279 i 


i -02 1 44 25 


i -060 43 20 


i-ioo 16 


1-142 12 


1-186 8 


1-232 _| 


1-280 38 o 


I-O2I 24 


1-061 19 


i-ioi 42 15 


1-143 II 


1-187 7 


1-233 3 


1-281 37 59 


1-022 23 


1-061 18 


I-I02 14 


1-144 41 10 


1-187 6 


2-233 2 


1-281 58 


I-O22 22 


1-062 17 


I -102 13 


1-144 9 


1-188 40 5 


1-234 i 


1-282 57 


I-O23 21 


1-062 16 


I-IO3 12 


1-145 8 


1-189 4 


1-235 39 o 


1-283 56 


1-023 44 20 


1-063 43 15 


I-I03 II 


1-146 7 


1-190 3 


1-236 38 59 


1-284 37 55 


1-024 19 


1-064 14 


1-104 42 10 


1-146 6 


1-190 2 


1-236 58 


1-285 54 


1-025 1 8 


1-064 13 


1-105 9 


*-*47 4 1 5 


I-IQI I 


1-237 57 


1-285 53 


1-025 17 


1-065 I2 


1-105 8 


1-148 4 


1-192 40 o 


1-238 56 


1-286 52 


1-026 1 6 


1-065 IT 


1-106 7 


1-148 3 


1-192 39 59 


1-239 3 8 55 


1-287 51 


1-026 44 15 


I 066 .43 10 


1-107 6 


I-I49 2 


I-I93 5 8 


1-239 54 


1-288 }7 50 


1-027 * 4 


1-067 9 


1-107 4 2 5 


I-I50 I 


I-I94 57 


1-240 53 


1-288 49 


1-028 13 


1-067 8 


1-108 4 


1-150 41 o 


i -195 56 


1-241 52 


1-289 48 


1-028 12 


1-068 7 


1-109 3 


1-151 40 59 


I-I95 39 55 


1-241 51 


1-290 47 


1-029 II 


1-069 6 


I-I09 2 


1-152 58 


1-196 54 


1-242 38 50 


1-291 46 


1-029 44 10 


1-069 43 5 


I-IIO I 


I-I5 2 57 


I-I97 53 


1-243 49 


1-291 37 45 


1-030 9 


1-070 4 


i 1 1 1 42 o 


I-I53 56 


I-I97 52 


1-244 48 


1-292 44 


1-031 8 


1-070 3 


i-iii 41 59 


I-I54 4 55 


1-198 51 


1-244 47 


1-293 43 


1-031 7 


1-071 2 


I-II2 58 


I-I54 54 


i -199 39 50 


1-245 46 


1-294 42 


1-032 6 


1-072 i 


1-113 57 


155 53 


i -199 49 


1-246 38 45 


1-295 4 1 


T '032 44 .5 


1-072 43 o 


1-113 56 


1-156 52 


I-2OO 48 


1-247 14 


1-295 37 4 


I '33 4 


1-073 42 59 


1-114 4i 55 


156 51 


i-2oi 47 


1-247 43 


1-296 39 


1-034 3 


1-074 58 


1-114 54 


157 4 50 


I-2O2 46 


1-248 42 


1-297 38 


1034 2 


1-074 57 


1-115 53 


1-158 49 


1-202 39 45 


1-249 41 


1-298 37 


I>0 35 i 


I '75 5 


1-116 52 


-158 48 


1-203 44 


1-250 38 40 


1-298 36 


i-35 44 o 


1-075 42 55 


1-116 51 


159 47 


1-204 43 


1-250 39 


1-299 37 35 


I '36 43 59 


1-076 54 


1-117 41 50 


160 46 


1-204 42 


1-251 38 


1-300 34 


1-037 58 


i-77 53 


I-II8 49 


161 40 45 


1-205 41 


1-252 37 


1-301 33 


i-37 57 


1-077 52 


1-118 48 


161 44 


1-206 39 40 


1-253 36 


1-302 32 


1-038 56 


1-078 51 


i-iiQ 47 


162 43 


1-207 39 


1-253 3 tS 35 


1-302 31 



70 

Table C 1 . 

AZIMUTH CORRESPONDING TO A AND B CORRECTION IN DEPARTURE. 



A & B Az. 


A & B Az. 


A & B Az. 


A & B Az. 


A & B Az. 


A&B Az. 


A&B Az. 
















i-33 37 3 


1-355 36 25 


1-410 35 21 


1-467 34 17 


1-527 33 13 


I-59I 32 9 


I-659 31 5 


1-304 29 


I-356 24 


1-411 35 20 


1-468 16 


1-528 16 


1-592 8 


1-660 4 


1-305 28 


1-357 23 


1-411 19 


1-469 34 15 


1-529 ii 


1-593 7 


1-661 3 


1-306 27 


1-358 22 


1-412 18 


1-470 14 


1-53 33 1 


1-594 6 


1-662 2 


1-306 26 


1-359 21 


1-413 17 


1-470 13 


I-53I 9 


1-595 32 5 


1-663 ! 


I-307 37 25 


1-360 36 20 


1-414 16 


1-471 12 


1-532 8 


1-596 4 


1-664 3 1 


1-308 24 


1-360 ~ 19 


1-415 35 15 


1-472 n 


1-533 7 


1-597 3 


1-665 3 59 


1-309 23 


1-361 18 


1-416 14 


1-473 34 10 


1-534 6 


1-598 2 


1-666 58 


I-309 22 


1-362 17 


I '4 I 7 13 


1-474 9 


1-535 33 5 


1-599 i 


1-668 57 


I-3IO 21 


1-363 16 


1-418 12 


1-475 8 


I-536 4 


i -600 32 o 


1-669 56 


1-311 37 20 


1-364 36 15 


1-418 II 


1-476 7 


1-537 3 


1-601 ^i 59 


1-670 30 55 


1-312 19 


1-365 M 


1-419 35 10 


1-477 6 


I-538 2 


1-602 ' 58 


1-671 54 


I-3I3 18 


1-365 13 


1-420 9 


I-478 34 5 


1-539 i 


1-603 57 


1-672 53 


I '3i3 17 


1-366 12 


1-421 8 


J> 479 4 


1-54 33 


1-604 56 


1-673 52 


1-314 16 


1-367 II 


1-422 7 


1-480 3 


1-541 32 59 


1-605 31 55 


1-674 51 


I-3I5 37 15 


1-368 36 TO 


1-423 6 


1-481 2 


I-542 5 8 


1-607 54 


I-675 3 50 


1-316 14 


I-369 ; 9 


*-424 35 5 


1-482 I 


1-543 57 


1-608 53 


1-676 49 


I-3I7 13 


1-370 8 


1-425 4 


1-483 34 o 


1-544 56 


1-609 52 


1-677 48 


1-317 12 


1-370 7 


1-425 3 


1-483 33 59 


1-545 32 55 


1-610 51 


1-679 47 


1-318 ii 


1-371 6 


1-426 2 


1-484 58 


i-54 54 


1-611 31 50 


i -680 46 


I-3I9 37 i 


1-372 36 5 


1-427 I 


1-485 57 


1-547 53 


1-612 49 


1-681 30 45 


1-320 9 


!'373 4 


1-428 35 o 


1-486 " 56 


I-548 52 


1-613 48 


1-682 44 


1-321 8 


1-374 3 


1-429 34 59 


!-4 8 7 33 55 


1-549 51 


1-614 47 


1-683 43 


1-321 7 


1-375 2 


1-430 58 


1-488 54 


1-550 32 50 


1-615 46 


1-684 42 


1-322 6 


1-375 i 


i-43i 57 


1-489 53 


i-55i 49 


1-616 31 45 


1-685 4 1 


1-323 37 5 


1-376 36 o 


1-432 56 


1-490 52 


1-552 4 8 


1-617 44 


1-686 30 40 


1-324 4 


J -377 35 59 


*-433 34 55 


1-491 51 


1-553 47 


1-618 43 


1-687 " 39 


1-325 3 


1-378 58 


1-433 54 


1-492 33 50 


1-554 46 


1-619 42 


1-689 38 


1-325 2 


1-379 57 


1-434 53 


1-493 49 


1-555 32 45 


1-620 41 


1-690 37 


1-326 i 


1-380 56 


J '435 52 


1-494 48 


I-556 44 


1-621 31 40 


1-691 36 


1-327 37 o 


1-381 35 55 


I-436 51 


1-495 47 


1-557 43 


1-622 39 


1-692 30 35 


1-328 36 59 


1-381 54 


!'437 34 50 


1-496 46 


I-558 42 


1-623 38 


1-693 34 


1-329 58 


1-382 53 


1-438 49 


!'497 33 45 


1-559 41 


1-624 37 


1-694 33 


I-329 57 


1-383 52 


1-439 4 8 


1-498 44 


1-560 32 40 


1-625 36 


1-695 32 


1-330 56 


1-384 5i 


1-440 47 


1-498 43 


1-561 39 


1-626 31 35 


1-696 31 


I-33I 36 55 


1-385 35 50 


1-441 46 


1-499 42 


1-562 38 


1-628 34 


1-698 30 30 


!'332 54 


1-386 49 


I '44 I 34 45 


1-500 41 


1-563 37 


1-629 33 


1-699 ~ 29 


1-333 53 


1-386 48 


1-442 44 


1-501 33 40 


1-564 36 


1-630 32 


1-700 28 


1-333 52 


1-387 47 


1 '443 43 


1-502 39 


1-565 32 35 


1-631 31 


1-701 27 


1-334 5i 


1-388 46 


1-444 42 


I-503 38 


1-566 34 


1-632 31 30 


1-702 26 


1-335 36 50 


1-389 35 45 


1-445 41 


1-504 37 


1-567 33 


1-633 29 


1-703 30 25 


I-336 49 


1-390 44 


1-446 34 40 


1-505 36 


1-568 32 


1-634 28 


1-704 24 


J -337 4 8 


I-39I 43 


I- 447 39 


1-506 33 35 


1-569 3i 


1-635 27 


1-706 23 


!-337 47 


1-392 42 


1-448 38 


I-507 34 


1-57 32 30 


1-636 26 


1-707 22 


1-338 46 


1-392 41 


I- 449 37 


1-508 33 


1-571 29 


1-637 3i 25 


1-708 21 


*-339 36 45 


1-393 35 4 


1-450 36 


1-509 32 


1-572 28 


1-638 24 


1-709 30 20 


1-340 44 


1-394 39 


1-45 34 35 


1-510 31 


1-573 27 


1-639 23 


I-7IO 19 


I '34 I 43 


1-395 3 8 


i-45i 34 


i-5ii 33 30 


1-574 2 6 


1-640 22 


1-711 18 


1-342 42 


1-396 37 


1-452 33 


1-512 29 


1-575 32 25 


1-641 21 


1-712 17 


1-342 41 


1-397 36 


1-453 32 


I-5I3 28 


1-576 24 


1-643 3 1 20 


1-714 16 


!'343 36 4 


!'398 35 35 


1-454 3i 


I-5I4 27 


1-577 23 


1-644 19 


I-7I5 30 15 


1-344 39 


1-398 34 


1-455 34 3 


I-5I5 26 


1-578 22 


1-645 1 8 


1-716 14 


*-345 38 


1-399 33 


1-456 29 


1-516 33 25 


1-579 21 


1-646 17 


1-717 13 


1-346 37 


1-400 32 


1-457 28 


1-517 24 


1-580 32 20 


1-647 16 


1-718 12 


1-346 36 


1-401 31 


1-458 27 


I-5I7 23 


1-581 19 


1-648 31 15 


I-7I9 II 


!'347 36 35 


I '42 35 3 


1-459 26 


1-518 22 


1-582 18 


1-649 14 


1-720 30 10 


I-348 34 


1-403 29 


1-460 34 25 


1-519 21 


1-583 i? 


1-650 13 


1-722 9 


1-349 33 


1-404 28 


1-460 24 


1-520 33 20 


1-584 16 


1-651 12 


1-723 8 


1-350 32 


1-404 27 


1-461 23 


1-521 19 


1-585 32 15 


1-652 II 


1-724 7 


I-35I 3i 


1-405 26 


1-462 22 


1-522 18 


1-586 14 


1-653 3 1 I0 


I-725 6 


!'35i 36 3 


1-406 35 25 


1-463 21 


1-523 17 


1-587 13 


1-654 9 


1-726 30 5 


1-352 29 


1-407 24 


1-464 34 20 


1-524 16 


1-588 1.2 


1-655 8 


1-727 4 


1-353 28 


1-408 23 


1-465 19 


1-525 33 Z 5 


1-589 II 


1-657 7 


1-729 3 


1-354 27 


1-409 22 


1-466 1 8 


1-526 14 


1-590 32 10 


1-658 6 


1-730 2 


1-355 26 


I-4IO 21 


1-467 17 


1-527 *3 


I-59I 9 


1-659 31 5 


I-73I r 



71 

Table C 1 . 

AZIMUTH CORRESPONDING TO A AND B CORRECTION IN DEPARTURE. 



A&B Az. 


A&B Az. 


A&B Az. 


A&B Az. 


A&B Az. 


A&B Az. 


A&B Az. 
















732 30 o 


810 28 55 


893 27 51 


1-981 26 47 


2-076 25 43 


2-179 24 39 


2-291 23 35 


733 29 59 


811 54 


894 27 50 


1-982 46 


2-078 42 


2-181 38 


2-293 34 


734 58 


813 53 


895 49 


1-984 26 45 


2-079 41 


2-182 37 


2-294 33 


736 57 


814 52 


897 48 


1-985 44 


2-081 25 40 


2-184 36 


2-296 32 


737 56 


'815 5i 


898 47 


1-987 43 


2-082 39 


2-186 24 35 


2-298 31 


738 29 55 


816 28 50 


899 46 


1-988 42 


2-084 38 


2-188 34 


2-300 23 30 


739 54 


818 49 


901 27 45 


1-990 41 


2-086 37 


2-189 33 


2-302 29 


74 53 


819 48 


902 44 


1-991 26 40 


2 087 36 


2-191 32 


2-303 28 


74 1 52 


820 47 


903 43 


1-993 39 


2-089 25 35 


2-193 3i 


2-305 27 


743 5i 


821 46 


905 42 


1-994 38 


2-090 34 


2-194 24 30 


2-307 26 


744 29 5 


823 28 45 


906 41 


1-995 37 


2-092 33 


2-196 29 


2-309 23 25 


745 49 


-824 44 


907 27 40 


1-997 3 6 


2-093 32 


2-198 28 


2-311 24 


746 48 


825 43 


909 39 


1-998 26 35 


2-095 31 


2-199 27 


2-3I3 23 


747 47 


826 42 


910 38 


2-000 34 


2-096 25 30 


2-2OI 26 


2-315 22 


748 46 


828 41 


9ii 37 


2-001 33 


2-098 29 


2'203 24 25 


2-316 21 


750 29 45 


829 28 40 


913 36 


2-003 32 


2-IOO 28 


.2-204 24 


2-318 23 2O 


751 44 


830 39 


914 27 35 


2-004 31 


2-IOI 27 


2-2O6 23 


2-320 19 


752 43 


832 38 


915 34 


2-006 26 30 


2-I03 26 


2-2O8 22 


2-322 18 


753 42 


833 37 


917 33 


2-007 29 


2-104 25 25 


2-2IO 21 


2-324 17 


754 41 


834 36 


918 32 


2-009 28 


2-106 24 


2-2II 24 2O 


2-326 16 


756 29 40 


835 28 35 


920 31 


2-OIO 27 


2-108 23 


2-213 J 9 


2-328 23 15 


757 39 


837 34 


921 27 30 


2-OII 26 


2-IO9 22 


2-215 l8 


2-329 14 


758 38 


838 33 


922 29 


2-OI3 26 25 


2-III 21 


2-216 17 


2-331 13 


759 37 


839 32 


924 28 


2-014 2 4 


2-II2 25 2O 


2-218 16 


2-333 12 


760 36 


840 31 


925 27 


2-OI6 23 


2-114 19 


2-220 24 15 


2-335 ii 


761 29 35 


842 28 30 


926 26 


2-OI7 22 


2-115 18 


2-222 14 


2-337 23 10 


763 34 


843 29 


928 27 25 


2-019 21 


2-117 17 


2-223 r 3 


2-339 9 


764 33 


844 28 


929 24 


2-020 26 20 


2-119 16 


2-225 I 2 


2-341 


765 32 


846 27 


93i 23 


2-O22 19 


2-120 25 15 


2-227 n 


2-343 7 


766 31 


847 26 


932 22 


2-023 18 


2-122 14 


2-229 24 10 


2-34.4 6 


767 29 30 


848 28 25 


933 21 


2-O25 17 


2-123 13 


2-230 9 


2-346 23 5 


769 29 


849 24 


1-935 27 20 


2-026 16 


2-I25 12 


2-232 8 


2-348 4 


770 28 


851 23 


1-936 19 


2-028 26 15 


2-127 n 


2-234 7 


2-35 3 


771 27 


852 22 


1-937 18 


2-O29 14 


2-128 25 10 


2-235 6 


2-352 2 


772 26 


853 21 


1-939 17 


2-031 I 3 


2-130 9 


2-237 24 5 


2-354 i 


773 29 25 


855 28 20 


940 16 


2-032 12 


2-131 8 


2-239 4 


2-356 23 o 


775 24 


856 19 


942 27 15 


2-034 II 


2-133 7 


2-241 3 


2-358 22 59 


776 23 


857 18 


943 H 


2-035 26 10 


2-135 6 


2-242 


2-360 58 


777 22 


858 17 


944 13 


2-037 9 


2-136 25 5 


2-244 I 


2-362 57 


778 2i 


860 16 


946 12 


2-038 8 


2-138 4 


2-246 24 o 


2-363 56 


780 29 20 


861 28 15 


947 ii 


2-040 7 


2-140 3 


2-248 23 59 


2-365 22 55 


781 19 


862 14 


949 27 10 


2-041 6 


2-141 2 


2-250 58 


2-367 54 


782 18 


864 13 


95 9 


2-043 26 5 


2-143 I 


2-251 57 


2-369 53 


783 17 


865 12 


951 8 


2-044 4 


2-144 25 o 


2-253 56 


2-371 52 


784 16 


866 ii 


953 7 


2-046 3 


2-146 24 59 


2-255 23 55 


2-373 5i 


786 29 15 


868 28 10 


954 6 


2-047 2 


2-148 58 


2-257 54 


2-375 22 50 


787 14 


869 9 


956 27 5 


2-049 i 


2-149 57 


2-258 53 


2-377 49 


788 13 


870 8 


957 4 


2-050 26 o 


2-151 56 


2-260 52 


2-379 48 


789 12 


871 7 


958 3 


2-052 25 59 


2-153 24 55 


2-262 51 


2-381 '47 


790 II 


873 6 


960 2 


2-053 58 


2-154 54 


2-264 2 3 5 


2-383 46 


792 29 10 


874 28 5 


96l I 


2-055 57 


2-156 53 


2-265 49 


2-385 22 45 


793 9 


875 4 


963 27 o 


2-056 56 


2-158 52 


2-267 48 


2-387 44 


794 * 


877 3 


964 26 59 


2-058 25 55 


2-159 5 1 


2-269 47 


2-389 43 


795 7 


878 2 


965 58 


2-059 54 


2-161 24 50 


2-271 46 


2-391 42 


797 6 


879 I 


967 57 


2-061 53 


2-163 49 


2-273 23 45 


2-392 41 


798 29 5 


881 28 o 


968 56 


2-062 52 


2-164 4 8 


2-274 44 


2-394 22 40 


799 4 


882 27 59 


970 26 55 


2-064 51 


2-166 47 


2-276 43 


2-396 39 


800 3 


883 58 


97 1 54 


2-065 25 50 


2-167 46 


2-278 4 2 


2-398 38 


802 2 


885 57 


972 53 


2-067 49 


2-169 24 45 


2-280 41 


2-400 37 


803 i 


886 56 


974 52 


2-069 48 


2-171 44 


2-282 23 40 


2-402 36 


804 29 o 


887 27 55 


975 5i 


2-070 47 


2-172 43 


2-283 39 


2-404 22 35 


805 28 59 


889 54 


977 26 50 


2-072 46 


2-174 42 


2-285 3 8 


2-406 34 


806 58 


890 53 


978 49 


2-073 25 45 


2-176 41 


2-287 37 


2-408 33 


808 57 


891 52 


980 48 


2-075 44 


2-177 24 40 


2-290 36 


2-410 32 


1-809 56 


893 5i 


981 47 


2-076 43 


2-179 39 


2-291 23 35 


2-412 31 



72 

Table C*. 

AZIMUTH CORRESPONDING TO A AND B CORRECTION IN DEPARTURE. 



A & B Az. 


A & B Az. 


A & B Az. 


A & B Az. 


A & I ; Az. 


A & H Az. 


A <$ B Az. 


t 














2-414 22 30 


2-549 21 25 


2-696 20 21 


2-858 19 17 


3-038 18 13 


3-240 17 9 


3-468 16 5 


2-416 20 


2-552 24 


2-699 20 20 


2-861 16 


3-041 12 


3-244 


3-472 4 


2-418 28 


2-554 23 


2-7OI 19 


2-864 19 15 


3-044 ii 


3-247 7 


3-476 s 


2-420 27 


2-556 22 


2-703 18 


2-866 14 


3-047 1 8 10 


3-251 6 


3-48o 2 


2-422 26 


2-558 21 


2-706 17 


2-869 13 


3-050 9 


3-254 17 5 


3-484 i 


2-424 22 25 


2-560 21 2O 


2-708 16 


2-872 12 


3-053 


3-257 4 


3-487 16 o 


2-426 24 


2-563 19 


2-711 20 15 


2-874 IT 


3-056 7 


3-26i 3 


3-491 15 59 


2-428 23 


2-565 18 


2-713 14 


2-877 *9 IO 


3-059 6 


3-264 2 


3-495 58 


2-430 22 


2-567 17 


2-715 13 


2-880 9 


3-062 1 8 5 


3-267 i 


3-499 57 


2-432 21 


2-569 If) 


2-718 12 


2-882' 8 


3-066 4 


3-271 17 o 


3-503 56 


2-434 22 2O 


2-571 21 15 


2-720 II 


2-885 7 


3-o69 3 


3-274 16 59 


3-507 15 55 


2-436 IQ 


2-574 M 


2-723 20 10 


2-888 6 


3-072 2 


3-278 58 


3-5io 54 


2-438 18 


2-576 13 


2-725 9 


2-891 19 5 


3-075 i 


3-281 57 


3-5I4 53 


2-440 17 


2-578 12 


2-728 


2-893 4 


3-078 18 o 


3-284 56 


3-5i8 52 


2-442 16 


2-580 II 


2-730 7 


2-896 3 


3-081 17 59 


3-288 16 55 


3-522 51 


2-444 22 15 


2-583 21 IO 


2-733 6 


2-899 2 


3-084 58 


3-291 54 


3-526 15 50 


2-446 14 


2-585 9 


2-735 20 5 


2-9OI I 


3-087 57 


3-295 53 


3-530 49 


2-448 13 


2-587 8 


2-737 4 


2-904 IQ 


3-090 56 


3-298 52 


3-534 48 


2-450 12 


2-589 7 


2-740 3 


2-907 18 59 


3-093 J 7 55 


3-302 51 


3-538 47 


2-452 II 


2-592 6 


2-742 2 


2-910 58 


3-096 54 


3-305 1 6 50 


3-542 |6 


2-454 2 2 10 


2-594 21 5 


2-745 i 


2-912 57 


3-099 53 


3-309 49 


3-546 15 45 


2'457 9 


2-596 4 


2-747 20 o 


2-915 56 


3-102 52 


3-312 48 


3-550 44 


2-459 


2-598 3 


2-750 19 59 


2-918 18 55 


3-105 51 


3'3!6 47 


3-554 43 


2-461 7 


2-6OI 2 


2-752 58 


2-921 54 


3-108 17 50 


3-3I9 46 


3-558 42 


2-463 6 


2-603 I 


2-755 57 


2-923 53 


3-111 49 


3-323 16 45 


3-562 41 


2-465 22 5 


2-605 21 


2-757 56 


2-926 52 


3-II5 4 8 


3-326 44 


3-566 15 40 


2-467 4 


2-607 20 59 


2-760 19 55 


2-929 51 


3-118 47 


3-330 43 


3-57 39 


2-469 3 


2-610 58 


2-762 54 


2-932 18 50 


3-121 46 


3-333 42 


3-574 38 


2-471 2 


2-612 57 


2-765 53 


2-935 49 


3-124 17 45 


3-337 4 1 


3-578 37 


2-473 i 


2-614 56 


2-767 52 


2-937 48 


3-127 44 


3-340 16 40 


3-582 36 


2-475 22 


2-616 20 55 


2-770 51 


2-940 47 


3-13 43 


3-344 39 


3-586 15 35 


2-477 21 59 


2-619 54 


2-773 19 50 


2-943 46 


3-133 42 


3-347 3 8 


3-590 34 


2-479 58 


2-621 53 


2-775 49 


2-946 18 45 


3 >I 36 41 


3-351 37 


3-594 33 


2-481 57 


2-623 52 


2-778 48 


2-949 44 


3-140 17 40 


3-354 36 


3-598 32 


2-483 56 


2-626 51 


2-780 47 


2-951 43 


3-143 39 


3-358 16 35 


3-602 31 


2-485 21 55 


2-628 20 50 


2-783 46 


2-954 42 


S-M 6 3 8 


3-362 34 


3-606 15 30 


2-488 54 


2-630 49 


2-785 19 45 


2-957 4i 


3-149 37 


3-365 33 


3-610 29 


2-490 53 


2-632 48 


2-788 44 


2-960 18 40 


3-I52 36 


3-369 32 


3-614 28 


2-492 52 


2-635 47 


2-790 43 


2-963 39 


3-I56 17 35 


3-372 31 


3-618 27 


2-494 5i 


2-637 46 


2-793 42 


2-966 38 


3-159 34 


3-376 16 30 


3-622 26 


2-496 21 50 


2-639 20 45 


2-795 41 


2-969 37 


3-162 33 


3-379 29 


3-626 15 25 


2-498 49 


2-642 44 


2-798 19 40 


2-971 36 


3-165 32 


3-383 28 


3-630 24 


2-500 48 


2-644 43 


2-801 39 


2-9/4 l8 35 


3-168 31 


3-387 27 


3-635 23 


2-502 47 


2-646 42 


2-803 38 


2-977 34 


3-172 17 30 


3-390 26 


3-639 22 


2-504 46 


2-649 41 


2-806 37 


2-980 33 


3-175 29 


3-394 l6 25 


3-643 21 


2-507 21 45 


2-651 20 40 


2-808 36 


2-983 32 


3-178 28 


3-398 24 


3-647 15 20 


2-509 44 


2-653 39 


2-811 19 35 


2-986 31 


3-181 27 


3-401 23 


3-65I 19 


2-511 43 


2-656 38 


2-813 34 


2-989 1 8 30 


3-184 26 


3-405 22 


3-655 18 


2-513 42 


2-658 37 


2-816 33 


2-992 29 


3-188 17 25 


3-409 21 


3-660 17 


2-515 4i 


2-660 36 


2-819 32 


2-994 28 


3-191 24 


3-412 16 20 


3-664 16 


2-517 21 40 


2-663 20 35 


2-821 31 


2-997 27 


3-194 23 


3-416 19 


3-668 15 15 


2-519 39 


2-665 34 


2-824 1 9 3 


3-000 26 


3-197 22 


3-420 18 


3-672 14 


2-521 38 


2-667 33 


2-826 29 


3-003 1 8 25 


3-2OI 21 


3-4 2 3 17 


3-676 13 


2-523 37 


2-670 32 


2-829 28 


3-006 24 


3-204 17 20 


3-427 16 


3-68l 12 


2-526 36 


2-672 31 


2-832 27 


3-009 23 


3-207 19 


3-431 16 15 


3-685 II 


2-528 21 35 


2-675 20 30 


2-834 26 


3-012 22 


3-211 18 


3-434 M 


3-689 15 10 


2-530 34 


2-677 29 


2-837 19 25 


3-015 21 


3-214 17 


3-438 13 


3-693 9 


2-532 33 


2-679 28 


2-840 24 


3-018 18 20 


3-217 16 


3-442 12 


3-698 8 


2-534 32 


2-682 27 


2-842 23 


3-021 19 


3-220 17 15 


3-446 ii 


3-702 7 


2-536 31 


2-684 26 


2-845 22 


3-024 1 8 


3-224 14 


3-450 1 6 10 


3-706 6 


2-539 21 30 


2-686 20 25 


2-848 21 


3-027 17 


3-227 13 


3-453 9 


3'7 10 15 5 


2-541 29 


2-689 24 


2-850 19 20 


3-030 16 


3-230 12 


3-457 8 


3-7I5 4 


2-543 28 


2-691 23 


2-853 19 


3-033 18 15 


3-234 " 


3-461 7 


3-7I9 3 


2-545 27 


2-694 22 


2-856 18 


3-036 14 


3-237 17 10 


3-465 6 


3-723 2 


2-547 26 


2-696 21 


2-858 17 


3-038 13 


3-240 9 


3-468 16 5 


3-728 i 



73 

Table C 1 . 
AZIMUTH CORRESPONDING TO A AND B CORRECTION IN DEPARTURE. 



A&B Az 


.A&B Az 


A&B Az. 


A&B Az. 


A & B Az. 


A&B Az. 


A&B Az. 


3-732 15 


4-<>36 13 5j 


4-3 8 4 12 5 


4-794 ii 47 


5-284 10 4 


5-881 9 39 


6-625 8 35 


3-736 14 5 
3-74I 5 


4-041 54 
4-046 53 


4-390 12 5 
4-396 4 


4-801 4 e 
4-808 ii 45 


5-292 4 
5-301 4 


5-891 38 
5-902 37 


6-638 34 
6-651 33 


3-745 5 


4-051 52 


4-401 4 


4-815 44 


5-309 10 4 


5-912 36 


6-665 32 


3-749 5 


4-056 5 1 


4-407 4 


4-822 43 


5-318 3 


5-923 9 35 


6-678 31 


3-754 !4 5 


4-061 13 50 
4-066 49 


4-4I3 4 
4-419 12 4 


4-829 4 
4-836 4 


5-335 3 


5-933 3 
5-944 3 


6-691 8 30 
6-704 29 


3-763 5. 


4-071 48 


4-425 4' 


4-843 ii 4 


5-343 3 


5-954 3 


6-718 28 


3-767 5 


4-076 47 


4-43I 4 


4-850 3 


5-352 10 3 


5-965 3 


6-731 27 


3-771 5 


4-081 46 


4-437 4 


4-857 3 


5'36i 3 


5-976 9 3 


6-745 26 


3-776 14 50 


4-087 13 45 


4-443 4 


4-864 3 


5-369 v 


5-986 2 


6-758 8 25 


3-780 49 


4-092 44 


4-449 12 40 


4-871 3 


5-378 3 


5-997 2 


6-772 24 


3-785 48 


4-097 43 


4-455 12 39 


4-879 n 3 


5*387 3 


6-ooS 2 


6-786 23 


3-789 47 


4-102 42 


4-461 38 


4-886 3 


5-395 1 30 


6-019 26 


6-799 22 


3'794 46 


4-107 41 


4-468 37 


4-893 3: 


5-404 29 


6-030 9 25 


6-813 21 


3-798 14 45 


4-113 13 40 


4-474 36 


4-901 32 


5-4I3 28 


6-040 2, 


6-827 8 20 


3-803 44 


4-n8 39 


4-480 12 35 


4-908 3 


5-422 27 


6-051 2: 


6-841 19 


3-807 43 


4-123 38 


4-486 34 


4-915 ii 30 


5-431 26 


6-062 22 


6-855 18 


3-812 42 


4-128 37 


4-492 33 


4-922 29 


5-440 10 25 


6-073 21 


6-869 17 


3'8i6 41 


4-133 36 


4-498 32 


4-930 28 


5-449 24 


.6-084 9 20 


6-883 16 


3-821 14 40 


4 -I 39 13 35 


4-504 3i 


4-937 27 


5-457 23 


6-095 9 


6-897 8 15 


3-825 39 


4-144 34 


4-511 12 30 


4-945 26 


5-466 22 


6-107 8 


6-911 14 


3-830 38 


4-I49 33 


4-5I7 29 


4-952 ii 25 


5-475 21 


6-118 7 


6-925 I-- 


3-834 37 


4-155 32 


4-523 28 


4-959 24 


5-484 10 20 


6-129 6 


6-939 12 


3-839 36 


4-160 31 


^529 27 


4-967 23 


5-494 9 


6-140 9 5 


6-954 ii 


3-844 14 35 


4-165 13 30 


^536 26 


4-974 22 


5-503 8 


6-151 4 


6-968 8 10 


3-848 34 


4-171 29 


4-542 12 25 


4-982 21 


5-5I2 7 


6-163 3 


6-983 9 


853 33 


4-176 28 


4-548 2 4 


4-989 ii 20 


5-521 6 


6-174 2 


6-997 


3-857 32 


.-181 27 


4-554 23 


4-997 19 


5-530 1 5 


6-186 ii 


7-012 7 


3-862 31 


4-187 26 


.-561 22 


5-005 1 8 


5-539 ' 


6-197 9 10 


7-026 6 


3-867 14 30 


4-192 13 25 


4-567 21 


012 17 




6-208 9 


7-041 8 5 


871 29 


4-I97 2 4 


4574 12 20 


020 16 


5-558 12 


6-220 8 


7-056 4 


3-876 28 


4-203 23 


4-580 19 


027 II 15 


5-567 II 


6-232 7 


7-071 3 


3-881 27 


2O8 22 


4-586 18 


035 14 


5-576 10 10 


6-243 6 


7-085 2 


3-885 26 


214 21 


4-593 17 


043 13 


5-586 9 


6-255 9 5 


7-100 i 


3-890 14 25 


219 13 2O 


4-599 16 


050 12 


5-595 8 


6-267 4 


7-115 8 o 


3-895 24 


225 19 


4-606 12 15 


058 II 


5-604 7 


6-278 3 


7-13 7 59 


"899 23 


230 18 


612 14 


066 ii 10 


5-614 6 


6-290 2 


7-146 58 


3-904 22 


236 17 


619 13 


074 9 


5-623 10 5 


6-302 i 


7-161 57 


3-909 21 


241 16 


625 12 


081 8 


5-633 4 


6-314 9 o 


7-I76 56 


3-914 14 20 


247 13 J 5 


632 II 


089 7 


5-642 3 


6-326 8 59 


7-i9i 7 55 


3-918 19 


252 14 


638 12 IO 


097 6 


5-652 2 


6-338 58 


7-207 54 


3-923 18 


258 13 


645 9 


105 ii 5 


5-662 I 


6-350 57 


7-222 53 


3-928 17 


263 12 


651 8 


113 4 


5-671 10 o 


6-362 56 


7-237 52 


3-933 16 


269 II 


4-658 7 


121 3 


5-681 9 59 


374 8 55 


7-253 5i 


3-937 M 15 


275 13 10 


4-665 6 


129 2 


691 58 


386 54 


7-269 7 50 


3-942 14 


280 9 


4-671 12 5 


136 I 


.700 57 


398 53 


7-284 49 


3-947 13 


286 8 


4-678 4 


145 ii o 


71 56 


410 52 


300 48 


3-952 12 


292 7 


4-685 3 


153 i 59 


720 9 55 


422 51 


316 47 


3-957 ii 


297 6 


4-691 2 


161 58 


73 54 


435 8 50 


332 46 


962 14 10 


303 13 5 


4-698 i 


169 '57 


74 53 


447 49 


34 8 7 45 


3-967 9 


39 4 


4-705 12 


177 56 


749 52 


460 48 


364 44 


3-971 8 


314 3 


4-711 ii 59 


185 10 55 


759 5i 


472 47 


380 43 


3-976 7 


4-320 


4-7i8 58 


193 54 


769 9 5 


-485 46 


396 42 


3-981 6 


4-326 i 


4-725 57 


201 53 


779 49 


497 8 45 


412 41 


3-986 14 5 


4-331 13 o 


4-732 56 


209 52 


789 48 


51 44 


429 7 40 


3-991 4 


4-337 12 59 


4-738 ii 55 


217 51 


799 47 


522 43 


445 39 


3-996 3 


4-343 5 8 


4-745 54 


226 10 50 


-809 46 


535 42 


-461 38 


OOI 2 


4-349 57 


4-752 53 


234 49 


820 9 45 


548 41 


478 37 


O06 I 


4-355 56 


4-759 52 


242 48 


830 44 


561 8 40 


495 36 


on 14 o 


4-360 12 55 


4-766 51 


5-250 47 


840 43 


573 39 


5ii 7 35 


4-016 13 59 


4-366 54 


4-773 ii 50 


5-259 46 


850 42 


586 38 


528 34 


02 1 58 


4-372 53 


4-780 49 


5-267 10 45 


860 41 


599 37 


545 33 


026 57 


4-378 52 


4-787 48 


5-275 44 


871 9 4 


612 36 


562 32 


4-031 56 


4-384 51 


4-794 47 


5-284 43 


881 39 


625 8 35 


579 3i 



74 

Table C 1 . 
AZIMUTH CORRESPONDING TO A AND B CORRECTION IN DEPARTURE. 



A & B Az. 


A & B Az. 


A & B Az. 


A & B Az. 


A & B Az. 


A & B Az. 


A & B Az . 
















7-60 7 30 


8-89 6 25 


10-71 5 20 


13-4 4 16 


17-9 3 12 


26-8 2 8 


53-7 ! 4 


7-61 29 


8-92 24 


10-75 19 


13-5 4 15 


18-0 ii 


27-1 7 


54-6 3 


7-63 28 


8-94 23 


10-78 18 


13-5 H 


18-1 3 10 


27-3 6 


55'4 2 


7-65 27 


8-96 22 


10-81 17 


13-6 13 


18-2 9 


27-5 2 5 


56-4 i 


7-66 26 


8-99 21 


10-85 16 


13-6 12 


18-3 8 


27-7 4 


57'3 i o 


7-68 7 25 


9-01 6 20 


10-88 5 15 


I3-7 II 


18-4 7 


27-9 3 


58-3 o 59 


7-70 24 


9-03 19 


10-92 14 


13-7 4 10 


18-5 6 


28-2 2 


59'3 58 


7.72 23 


9-06 18 


10-95 13 


13-8 9 


18-6 3 5 


28-4 i 


^- ** 

00-3 57 


7.73 22 


9-08 17 


10-99 12 


13-8 8 


18-7 4 


28-6 2 


61-4 56 


7-75 21 


9-n 16 


11-02 II 


13-9 7 


18-8 3 


28-9 i 59 


62-5 o 55 


7-77 7 20 


9-13 6 15 


11-06 5 10 


14-0 6 


18-9 2 


29-1 58 


6 3'7 54 


7-79 19 


9-16 14 


11-10 9 


14-0 4 5 


19-0 i 


29-4 57 


64-9 53 


7-81 18 


9-18 13 


11-13 8 


14-1 4 


19-1 3 o 


29-6 56 


66-1 52 


7-82 17 


9-21 12 


11-17 7 


14-1 3 


19-2 2 59 


29-9 i 55 


67-4 5i 


7-84 16 


9-23 II 


11-20 6 


14-2 2 


19-3 58 


30-1 54 


68-7 o 50 


7-86 7 15 


9-26 6 10 


11-24 5 5 


14-2 I 


19-4 57 


3-4 53 


70-2 49 


7-88 14 


9-28 9 


11-28 4 


14-3 4 o 


19-5 56 


30-7 52 


71-6 48 


7-90 13 


9-31 8 


11-32 3 


M'4 3 59 


19-6 2 55 




73" 1 47 


7-92 12 


9-33 7 


n-35 2 


14-4 58 


19-7 54 


31-2 i 50 


74-7 46 


7-93 ii 


9-36 6 


11-39 i 


I4'5 57 


19-9 53 


SI'S 49 


76-4 o 45 


7-95 7 i 


9-38 6 5 


11-43 5 o 


14-5 56 


2O-O 52 


31-8 48 


78-1 44 


7.97 9 


9-41 4 


n-47 4 59 


14-6 3 55 


2O-I 51 


32-1 47 


79-9 43 


7.99 


9-44 3 


ii-5i 58 


J 4'7 54 


20-2 2 50 


32-4 46 


81-8 42 


8-01 7 


9-46 2 


n-55 57 


14-7 53 


20-3 49 


32-7 ! 45 


83-8 41 


8-03 6 


9-49 i 


n-59 56 


14-8 52 


20-4 48 


33' 44 


85-9 o 40 


8-05 7 5 


9-51 6 o 


11-62 4 55 


14-9 5i 


20-6 47 


33'4 43 


88-1 39 


8-07 4 


9-54 5 59 


11-67 54 


14-9 3 50 


20-7 46 


33'7 42 


90-5 38 


8-09 3 


9-57 58 


ii-7i 53 


15-0 49 


20-8 2 45 


34' 4 1 


92-9 37 


8-10 2 


9-59 57 


n-74 52 


15-1 48 


20-9 44 


34-4 i 40 


95-5 36 


8-12 I 


9-62 56 


11-78 51 


i5-i 47 


21-1 43 


34'7 39 


98-2 o 35 


8-14 7 o 


9-65 5 55 


11-83 4 50 


15-2 46 


21-2 42 


35-i 38 


101 34 


8-16 6 59 


9-68 54 


11-87 49 


!5'3 3 45 


21-3 41 


35-4 37 


I0 4 33 


8-18 58 


97 53 


11-91 48 


15-3 44 


21-5 2 4 


35-8 36 


107 32 


8-20 57 


9-73 52 


n-95 47 


!5'4 43 


21-6 39 


36-2 i 35 


in 31 


8-22 56 


9-76 51 


ii-99 46 


15-5 42 


21-7 38 


36-6 34 


115 o 30 


8-24 6 55 


9-79 5 5 


12-03 4 45 


15-5 41 


21-9 37 


37- 33 


118 29 


8-26 54 


9-82 49 


12-08 44 


15-6 3 4 


22-0 36 


37-4 32 


123 28 


8-28 53 


9-84 48 


12-12 43 


15-7 39 


22-2 2 35 


37-8 31 


127 27 


8-30 52 


9-87 47 


12-16 42 


15-7 38 


22-3 34 


38-2 i 30 


132 26 


8-32 51 


9-90 46 


12-21 41 


15-8 37 


22-5 33 


38-6 29 


138 o 25 


8-34 6 50 


9-93 5 45 


12-25 4 40 


15-9 36 


22-6 32 


39-0 28 


143 24 


8-36 49 


9-96 44 


12-29 39 


16-0 3 35 


22-8 31 


39-5 27 


M9 23 


8-39 48 


9-99 43 


12-34 38 


16-0 34 


22-9 2 30 


40-0 26 


156 22 


8-41 47 


IO-O2 42 


12-38 37 


16-1 33 


23-1 29 


40-4 i 25 


164 21 


8-43 46 


10-05 4 1 


12-43 36 


16-2 32 


23-2 28 


4-9 24 


172 o 20 


8-45 6 45 


1 0-08 5 40 


12-47 4 35 


16-3 31 


23-4 27 


4I-4 23 


181 19 


8-47 44 


10-11 39 


12-52 34 


16-3 3 30 


23-5 26 


41-9 22 


191 18 


8-49 43 


10-13 38 


12-57 33 


16-4 29 


23-7 2 25 


42-4 21 


202 17 


8-51 42 


10-17 37 


12-61 32 


16-5 28 


23-9 24 


43-0 I 2O 


215 16 


8-53 41 


10-20 36 


12-66 31 


16-6 27 


24-0 23 


43-5 19 


229 o 15 


8-56 6 40 


10-23 5 35 


12-71 4 30 


16-7 26 


24-2 22 


44-1 18 


246 14 


8-58 39 


10-26 34 


12-75 29 


16-7 3 25 


24-4 21 


44-6 17 


264 13 


8-60 38 


10-29 33 


12-80 28 


16-8 24 


24-5 2 20 


45-2 16 


286 12 


8-62 37 


10-32 32 


12-85 27 


16-9 23 


2 4 -7 19 


45-8 i 15 


3*3 


3-64 36 




12-90 26 


17-0 22 


24-9 18 


46-4 14 


344 o !0 


8-66 6 35 


10-39 5 3 


12-95 4 25 


I7-I 21 


25-1 17 


47-i 13 


382 9 


8-69 34 


10-42 29 


13-00 24 


17-2 3 20 


25-2 16 


47-7 12 


430 8 


8-71 33 


10-45 28 


13-05 23 


17-3 19 


25-5 2 15 


48-4 ii 


49i 7 


8-73 32 


10-48 27 


13-10 22 


17-3 18 


25-6 14 


49-1 i 10 


573 6 


8-75 3i 


10-51 26 


I3-I5 21 


17-4 17 


25-8 13 


49-8 9 


688 o 5 


8-78 6 30 


io-55 5 25 


13-20 4 20 


17-5 16 


26-0 12 


50-5 8 


859 4 


8-80 29 


10-58 24 


13-25 19 


17-6 3 15 


26-2 II 




1146 3 


8-82 28 


10-61 23 


13-30 18 


17.7 14 


26-4 2 10 


52-1 6 


1719 2 


8-85 27 


10-65 22 


I3-35 i? 


17-8 13 


26-6 9 


52-9 i 5 


3438 i 


8-87 26 


10-68 21 


13-40 16 


I7-9 12 


26-8 8 


53'7 4 


Infinite o o 



75 
Table O 

POSITION-LINKS CORRESPONDING TO THE A AND B CORRECTION. FOR USE 
WITH THE PLANE-SCALE CHART IN THE SUMNER PROBLEM. 

Name the position-line according to the name of the A and B correction, and contrary to the 
name of the bearing of the body observed. 



AandB 
Correction. 


Position- 
Hues. 


AandB 
Correction. I 


J< 
l fl 


A and B 
Correction. 1 


Position- 
lines. 


AandB 
Correction. I 


Position- 
lines. 


A and B 
Correction. 


Position, 
lines. 


AandB 
Correction. 1 


Position- 
lines. 


A and B 
Correction. J 


Position- 
lines. 


AandB 
Correction. I 


Poeition- 
liues. 


i 

oo = 




= O'O 


25- 


o 

14-0 


50 = 


26-6 


i 

75 = 


36-9 


1-00 = 


o 


1-42 = 





1-92 = 


,o 

= 62-5 


' O 

4-2 = 76-6 


or 


0'6 


26 


14-6 


51 


27-0 


76 


37'2 


I'OI 


45'3 


1-44 


55'2 


1-94 


627 


4'4 


77'2 


02 


I-I 


27 


15-1 


52 


27*5 


77 


37-6 


1-02 


45-6 


1-46 


55-6 


1-96 


63-0 


4'6 


777 


03 


17 


28 


I 5 6 


53 


279 


78 


38-0 


1-03 


45'8 


1-48 


56-0 


1-98 


63-2 


4-8 


78-2 


4 


2-3 


29 


1 6'2 


54 


28-4 


79 


38-3 


I'0 4 


46-1 




56-3 


2'OO 


63-4 


5-0 


787 


05 


2-9 


30 


167 


55 


28-8 


80 


387 


1-05 


46-4 


1-52 


567 


2-05 


64-0 


5'5 


797 


06 


3-4 


31 


17-2 


56 


29-2 


81 


39-0 


I -06 


467 






2'10 


64^5 


6-0 


8o $ 5 


07 




32 


177 


'57 


297 


82 


39'4 


1-07 


46-9 


J-56 


57'3 


2-15 


65-1 


6*5 


81-3 


08 


4'6 


33 


18*3 


58 


30-1 


83 


397 


I 08 


47'2 


r-58 


577 


2-20 


65-6 


7-0 


81-9 


09 


5-i 


34 


18-8 


59 


30-5 


84 


40-0 


I'lO 


477 


1-60 


58-0 


2-25 


66-0 


8-0 


82-9 


ro 


57 


'35 


193 


60 


31-0 


85 


40-4 


I-I2 


48-2 


1-62 


58-3 


2-30 


66-5 


9-0 


837 


II 


63 


36 


19-8 


6 1 


3i'4 


86 


407 


I'I4 


487 


1-64 


58-6 


2-40 


67-4 


io-o 


84*3 


12 


6-8 


37 


20-3 


62 


31-8 


87 


41-0 


1-16 


49-2 


1-66 


58*9 


2-50 


68-2 


II'O 


84-8 


'3 


7'4 


38 


20-8 


63 


32-2 


88 




1-18 


497 


r68 


59'2 


2'60 


69-0 


I2'O 


85-2 


M 


8-0 


'39 


21 3 


64 


32-6 


89 


417 


I'20 


50-2 


170 


59'5 


270 


697 


13-0 


85-6 


'IS 


8-5 


40 


21-8 


'65 


33'0 


90 


42-0 


I'22 


507 


172 


59'8 


2'80 


70-3 


15-0 


86-2 


16 


91 


41 


223 


66 


33'4 


91 


42-3 


I-2 4 




174 


60- 1 


2*9O 


71-0 


I7-0 


86-6 


17 


9-6 


42 


22-8 


67 


338 


92 


42 6 


1-26 


51-6 


176 


60-4 


3-00 


71-6 


20-0 


87-1 


18 


IO'2 


43 


23-3 


58 




93 


42-9 


128 


52-0 


178 


607 




72-1 


25-0 


877 


19 


10-8 


'44 


237 


69 


34'6 


94 




1-30 


52-4 


1-80 


60-9 


3'20 


72-6 


3 0-0 


88-1 


20 


ii'3 


45 


24-2 


70 


35-o 


95 


43'5 


1-32 


52-9 


1-82 


61-2 


3-30 


73'i 


4O'O 


88-6 


21 




46 


247 


71 


35'4 


96 


43-8 


1-34 


533 


1-84 


61-5 




73-6 


50'0 


88-9 


22 I2'4 


47 25-2 


72 


35-8 


97 


44-1 


1-36 


537 


1-86 


617 


3-60 


74-5 


lOO'O 


89-4 


23 I3-0 


48 


25-6 


73 


36-r 


98 


44*4 


I- 3 8 


54' i 


r88 


62-0 


3-80 


75'3 


2OO'O 


897 


24 13 5 


49 26-1 


74 


36-5 


99 


447 


I' 4 


54'5 


1-90 


62-2 


4-00 


76-0 


nfinite 


90-0 



It must be borne in mind that this table does not give the true geographical lines of position, 
but lines of position which will give the same result as to latitude and longitude on a plane chart 
as the true lines of position would give on a Mercator's chart. It is given here for the purpose of 
saving the trouble of getting out a chart. All that is required for plotting the Sumner position 
will be a horizontal line in the work-book representing the D.R. latitude, and a perpendicular line 
to the former for use in laying off the position-lines by a protractor. On the horizontal line set 
off the points of two longitudes at a distance from one another of, say, i in. to 10' of longitude. 
From these two points lay down the Sumner lines, and from the point where they intersect 
draw a perpendicular to the line of D.R. latitudes. The longitude at the point struck by the 
.perpendicular is the longitude required, and can be measured from either of the points of 
longitude. The same scale is used for the latitude as for the longitude. 

A small 5 in. boxwood protractor rule with a diagonal scale of inches for measuring to 
rfo part of an inch may be bought for is., and is the only instrument which will be required. 

To find the tme position-line from this table consider the A and B correction as a diff. 
long., the dep corresponding to this diff. long, will then give the true line of position, 
and will give the same position i e., latitude and longitude on the Mercator chart that the other 
4ines of position give on the plane chart. 

Example for true position-line : In lat 47 S. a.m. sun's obsn., when A and B cor. d. long, 
85' N. dep = '58' N. = true position-line N. 30-1 W. 



76 



Table D. 

SHOWING THE ERROR PRODUCED IN THE TIME OR LONGITUDE sv AN 

ALTITUDE. 



ERROR OF i' IN THE- 





AZIMUTHS. 


Lat. 






90 


89 


88 


87 


86 


85 


84 


83" 


82 


81 


80 


79 78 

i I 


77 


76 





S. 


s. 


S. 


s. 


S. 


s. 


S. 


S. 


S. 

















4-00 


4-00 


4'00 


4-01 


4-01 


4-02 


4'02 




4-04 


4-05 


4-06 


4-07 


4-09 


4-10 




i 


4-00 


4-00 


4'00 


4-01 


4-01 


4-02 


4'02 


4-03 


4-04 


4*05 


4*06 


4-08 


4-09 


4-11 


4'12 


2 


4-00 


4-00 


4'00 


4-01 


4-01 


4-02 


4'02 


4^3 


4-04 


4-05 


4-06 


4-08 


4-09 


4-11 


4'12 


3 


4.01 


4-01 


4'01 


4-01 


4-02 


4-02 


4'3 


4-04 


4-04 


4-06 


4-07 


4-08 


4-09 


4-11 




4 


4-01 


4-01 


4-01 


4-02 


4*02 


4*3 


4*03 


4-04 


4'5 


4-06 


4-07 


4-08 


4-10 


4-12 


4' J 3 


5 


4-01 


4-02 


4-02 


4-02 


4-03 


4*3 


4-04 


4-05 


4-05 


4 07 


4-08 


4-09 


4-10 


4-12 


4 14 


6 


4-02 


4-02 


4-02 


4*03 


4*03 


4-04 


4-04 


4-05 


4'06 


4-07 


4-08 


4*io 


4-11 


4' J 3 


4^5 


7 


4"3 


4'>3 


4'3 


4-04 


4-04 


4-05 


4*05 


4-06 


4-07 


4 08 


4-09 


4n 


4-12 


4-14 




8 


4-04 


4-04 


4-04 


4-04 


4 '05 


4-05 


4'o6 


4-07 


4-08 


4-09 


4 io 


4-11 






4*16 


9 


4*05 




4-05 


4-06 


4 o6 


4-07 


4-07 


4-08 


4-09 


4-10 


4-11 




4-14 


4-16 


4-17 


10 


4-06 


4-06 


4-06 


4-07 


4-07 


4-08 


4-08 


4-09 


4-10 


4-11 


4-12 


4-14 




4-17 


4-19 


ii 


4-07 


4-08 


4*08 


4-08 


4-08 


4-09 


4-10 


4-11 


4-11 


4-13 


4-14 


4-15 


4-17 


4-18 


4-20 


12 


4-09 


4-09 


4*09 


4-09 


4-10 


4-10 


4-11 


4-12 


4' r 3 


4-14 




4-17 


4-18 


4-20 


4'2I 


13 


4-10 


4-11 


4-11 


4-11 


4-12 


4-12 


4*13 


4-14 


4'i5 


4-16 


4* J 7 


4-18 


4-20 


4-21 




M 


4-12 


4-12 


4-12 


4*13 




4-14 


4-15 




4-16 


4-17 


4-19 


4-20 


4-21 


4*23 


4' 2 5 


15 


4-14 


4-14 


4-14 


4 t:t 5 


4'i5 


4-16 


4-16 


4-17 


4-18 


4-19 


4-20 


4-22 






4-27 


16 


4-16 


4-16 


4-16 


4-17 


4-17 


4-18 


4-18 


4-19 


4-20 


4-21 


4*23 


4*24 


4*25 


4-27 


4-29 


17 


4-18 


4-18 


4-19 


4-19 


4-19 


4-20 


4-21 


4-21 


4-22 


4-23 


4-25 


4-26 


4-28 


4-29 




18 


4-21 


4-21 


4-21 


4'2I 


4-22 


4-22 


4-23 


4-24 


4-25 


4-26 


4-27 


4-28 


4-30 


4*32 


4'33 


19 


4' 2 3 




4*23 


4-24 


4*24 


4' 2 5 


4-25 


4-26 


4-27 


4-28 


4-30 


4-31 


4-32 


4*34 


4-36 


20 


4-26 


J'26 


4-26 


4-26 


4*27 


4*27 


4-28 


4-29 


4*30 


4'S 1 




4'34 


4*35 


4'37 


4'39 


21 


4-28 


4-29 


4-29 


4-29 


4'3 


4'3<> 


4-31 


4'32 


4'33 


4'34 


4'35 


4*36 


4'38 


4-40 


4-42 


22 


4*31 


4-31 


4*32 


4*32 


4'32 


4'33 


4'34 


4*35 


4-36 


4'37 


4'38 


4'39 


4-41 


4'43 


4'45 


23 


4'34 


4'35 


4*35 


4*35 


4-36 


4-36 


4'37 


438 


4'39 


4-40 


4-41 


4'43 


4*44 




4-48 


24 


4-38 






4'38 


4*39 


4-40 


4-40 


4-41 


4-42 


4'43 


4'45 


4-46 


4-48 


4'49 




25 


4-41 


4-41 


4*42 


4*42 


4-42 


4'43 


4*44 


4'45 


4-46 


4*47 


4-48 


4*50 




4*53 


4*55 


26 


4*45 


4*45 


4'45 


4*46 


4-46 


4*47 


4'47 


4-48 


4*49 


4-5! 


4-52 


4'53 


4*55 


4'57 


4'59 


27 


4'49 


4'49 


4'49 


4'49 


4-50 


4-51 


4*51 


4-52 


4'53 


4'55 


4-56 


4'57 


4'59 


4-61 


4-63 


28 


4*53 


4'53 


4'53 


4'54 


4'54 


4'55 


4' 55 


4-56 


4'57 


4'59 


4-60 


4-62 


4-63 


4-65 


4-67 


29 


4'57 


4'57 


4*58 


4'58 


4-58 


4*59 


4'6o 


4-61 


4-62 


4-63 


4-64 


4-66 


4-68 


4-69 


471 


30 


4-62 


4-62 


4-62 


4-63 


4-63 


4-64 


4-64 


4-65 


4-66 


4-68 


4-69 


471 


472 


474 


476 


31 


4-67 


4*67 


4-67 


4-67 


4-68 


4-68 


4-69 


470 


471 


472 


474 


475 


477 


479 


4-81 


32 


472 


472 


472 


472 


473 


473 


474 


475 


476 


478 


479 


4 -8o 


4-82 


4-84 


4-86 


33 


477 


477 


477 


478 


478 


479 


4'8o 


4'8i 


4-82 


4*83 


4-84 


4-86 


4-88 


4-89 


-V92 


34 


4-82 


4-82 


4-83 


4-83 


4-84 


4-84 


4-85 


4-86 


4-87 


4-89 


4-90 


4-92 


4'93 


4'95 


4 '97 


35 


4-88 


4-88 


4-89 


4-89 


4*90 


4-90 


4-91 


4-92 


4'93 


4'94 


4-96 


4*97 


4*99 


5*01 


5-03 


36 


4'94 


4*95 


4*95 


4'95 


4-96 


4-96 


4 '97 


4-98 


4'99 


5-01 


5-02 


5'04 


5'5 


5-07 


5-10 


37 




5-01 


5*oi 


5'O2 




5-03 


5-04 


5'5 


5-06 


5-07 


5'09 




5'12 


5'M 


5*16 


38 


5-08 


5-08 




5-08 


5-09 


5-10 


5'io 


5-11 




5'i4 




5' 1 ? 


5-19 


5-21 


5-23 


39 






5'*5 


5-15 


5-16 


5^7 


5-18 


5-18 


5-20 




5-23 


5' 2 4 


5-26 


5-28 


5-30 


40 


5-22 


5'22 


5-22 


5-23 


5-23 


5-24 




5-26 


5-27 


5*29 




5*32 


5'34 


5-36 


5-38 


41 


5-30 


5-30 


5*30 


5*31 


S'3 1 


5'32 


5]33 


5'34 


5'35 


5'37 


5-38 


5*4 


5-42 


544 


5-46 


42 


5-38 


5-38 


5*39 


5'39 


5*4 






5-42 


5'44 


5'45 


5'47 


5-48 


5'5 


5'5 2 


5'55 


43 


5'47 


5'47 


5'47 


5'48 


5*48 


5*49 


5*50 


5*51 


5'5 2 


5*54 


5'55 


5'57 


5'59 


5*61 


5-64 


44 


5-56 


5-56 


5'56 


5'57 


5'57 


5*58 


5'59 


5'6o 


5*62 


5-63 


5-65 


5-66 


5-68 


57 r 


573 


45 


5-66 


5-66 




5-66 


5-67 


5'68 




570 


571 


573 


574 


576 


578 


5'8i 


5-83 


46 


576 


576 


576 


577 


577 


578 


579 


5-80 


5-81 


5-83 


5*85 


5'87 


5-89 


5-91 


5'93 


47 


5-87 


5-87 


5-87 


5-87 


5-88 




5-90 




5'9 2 


5'94 


5-96 


5'97 


6'oo 


6'O2 


6*04 


48 


5-98 


5-98 


5-98 


5 '99 


5*99 


6-00 


6 - oi 


6'O2 


6*04 


6-05 


6*07 


6-09 


6-n 


6-14 


6-16 


49 


6*10 


6*10 


6-10 


6*ii 


6-n 


6-12 


6-13 


6*14 


6-16 


617 


6*19 


6-21 


6-23 


6-26 


6-28 




6-22 


6'22 


6-23 


6-23 


6-24 


6-25 


6-26 


6-27 


.6-28 


6-30 


6-32 


6-34 


6-36 


6-39 


6-41 


51 


6-36 


6-36 


6-36 


6-36 


5-37 


6-38 


6'39 


6*40 


6-42 


6-44 


6-45 


6-48 


6*50 


6-52 


6'55 


52 


6-50 


6-50 


6*50 


6-51 


6-51 


6-52 


6-53 


6-55 


6-56 


6-58 


6-60 


6-62 


6-64 


6-67 


670 


53 


6-65 


6-65 


6-65 


6-66 


6-66 


6-67 


6-68 


670 


671 


673 


675 


677 


6-80 


6-82 


6-85 


54 


6-81 


6-81 


6-81 


6-81 


6-82 


6-83 


6-84 


6-86 


6-87 


6-89 


6-91 


6'93 


6-96 


6-98 


7'oi 


55 


6-97 


6-97 


6-98 


6-98 


6-99 


7-00 


7-01 


7'3 


7-04 


7-06 


7-08 


7-10 


7' X 3 


7-16 


7-19 


56 


7-15 


7*15 


7-16 


7-16 


7-17 


7-18 


7-19 


7-21 


7-22 


7-24 


7-26 


7-29 


7*31 


7*34 


7'37 


57 


7'34 


7'35 


7*35 


7*35 




7'37 


7-38 


7-40 


7-42 


7*44 


7H6 


7-48 


7-51 


7'54 


7'57 


58 


7*55 


7'55 


7'55 


7'56 


7*57 


7-58 


7*59 


7-61 


7 :f 


7-64 


7-66 


7-69 


772 


775 


778 


59 


777 


777 


777 


778 


779 


7-80 


7-81 


7-82 




7-86 


7-89 


7-91 


7*94 


7'97 


8-00 


60 


8-00 


8-00 


8-00 


S'oi 


8'02 


8-03 


8-04 


8-06 


8-os 


8-10 


8-12 


8-15 


8-18 


8-21 


8-24 


To convert time into longitude divide by 4. Thus 8*00 s. -f- 4 = 2' long. 



77 



Table D. 

SHOWING THE ERROR PRODUCED IN THE TIME OR LONGITUDE BY AN ERROR OF i 1 

ALTITUDE. 



IN THK 



Lat 


AZIMUTHS. 


75 


74 


73 


72 


71 


70 


69 


*63 D 


67 


56 


65 


61 


63 


62 


6P 





S. 


S 


S. 


S. 



























4-14 


4-16 


4-18 


4'2I 


4-23 


4-26 


4-28 


4-31 


4*35 


4-38 


S, 

4-41 


S. 

4'45 


S. 
4*49 


S. 

4*53 


S. 

4*57 


I 


4-14 


4-16 


4-18 


4'2I 


4-23 


4-26 


4-29 


4*31 


4'35 


4-38 


4-41 


4*45 


4'49 


4'53 


4'57 


2 


4-14 


4-16 


4-19 


4'2I 


4'23 


4-26 


4-29 


4*32 


4'35 


4-38 


4*42 


4'45 


4 '49 


4*53 


4*58 


3 


4-15 


4-17 


4-19 


4'2I 


4-24 


4-26 


4-29 


4*32 


4'35 


4-38 


4-42 


4-46 


4'50 


4*54 


4-58 


4 


4'*5 


4-17 


4-19 


4'22 


4-24 


4'27 


4'3 


4-32 


4-36 


4-39 


4-42 


4-46 


4*50 


4'54 


4-58 


5 


4-16 


4-18 


4-20 


4*22 


4'25 


4*27 


4-30 


4'33 


4'3 6 


4-40 


4 f 43 


4'47 


4*51 


4'55 


4'59 


6 


4-16 


4-18 


4-21 


4*23 


4-25 


4-28 


4'3i 


4*34 


4'37 


4-40 


4'44 


4'47 


4'5i 


4-56 


4'6o 


7 


4-17 


4-19 


4-21 


4-24 


4-26 


4-29 


4-32 


4-35 


4-38 


4-41 


4*45 


4'48 


4'52 


4-56 


4-61 


8 


4-18 


4-20 


4-22 


4*25 


4-27 


4-30 


4'33 


4 f 36 


4'39 


4-42 


4M6 


4'49 


4'53 


4*57 


4-62 


9 


4-19 


4-21 


4*23 


4'26 


4-28 


4'3i 


4'34 


4'37 


4-40 


4-43 


4'47 


4'5i 


4*55 


4'59 


4-63 


10 


4-20 


4'23 


4*25 


4-27 


4-30 


4'32 


4*35 


4-38 


4-41 


4*45 


4-48 


4-52 


4-56 


4 '60 


4-64 


ii 


4-22 


4-24 


4-26 


4-28 


4*3* 


4'34 


4-36 


4'39 


4'43 


4H6 


4*50 


4*53 


4*57 


4-62 


4-66 


12 


4-23 


4'25 


4-28 


4'3 


4-32 


4'35 


4-38 


4-41 


4'44 


4H8 


4'5i 


4'55 


4'59 


4-63 


4'68 


13 


4' 2 5 


4-27 


4-29 


4-32 


4*34 


4'37 


4-40 


4'43 


4-46 


4'49 


4'53 


4*57 


4-61 


4-65 


4-69 


H 


4-27 


4-29 


4'3* 


4'33 


4'36 


4'39 


4*42 


4*45 


4'48 


4'5i 


4'55 


4'59 


4-63 


4-67 


471 


15 


4-29 


4'3i 


4'33 


4'35 


438 


4-41 


4*44 


4*47 


4*50 


4'53 


4'57 


4'6i 


4-65 


4-69 


473 


16 


4*31 


4'33 


4'35 


4-38 


4-40 


4'43 


4-46 


4'49 


4-52 


4-56 


4*59 


4'63 


4-67 


471 


476 


*7 


4'33 


4'35 


4'37 


4-40 


4-42 


4'45 


4H8 


4'5i 


4'54 


4-58 


4-62 


4-65 


4-69 


474 


478 


18 


4'35 


4-38 


4-40 


4*42 


4*45 


4H8 


4'5i 


4'54 


4'57 


4'6o 


4-64 


4-68 


472 


476 


4 -8t 


19 


4-38 


4-40 


4'42 


4*45 


4'47 


4'50 


4'53 


4-56 


4'6o 


4'63 


4-67 


471 


475 


479 


4-84 


20 


4-41 


4'43 


4'45 


4-48 


4'50 


4*53 


4-56 


4*59 


4-62 


4-66 


470 


474 


478 


4-82 


4-87 


21 


4'44 


4-46 


4-48 


4*5i 


4'53 


4'56 


4'59 


4-62 


4-65 


4-69 


473 


477 


4-81 


4'85 


4-90 


22 


4*47 


4'49 


4'5i 


4'54 


4-56 


4'59 


4-62 


4-65 


4-69 


472 


476 


4-80 


4-84 


4-89 


4'93 


23 


4'50 


4'52 


4'54 


4'57 


4-60 


4-62 


4-65 


4-69 


4-72 


476 


479 


4*83 


4-88 


4-92 


4*97 


24 


4'53 


4-56 


4-58 


4-60 


4-63 


4-66 


4-69 


4-72 


476 


479 


4*83 


4-87 


4-91 


4-96 


5'or 


25 


4'57 


4'59 


4-62 


4-64 


4-67 


4*7 


4'73 


4-76 


479 


4-83 


4-87 


4'9i 


4'95 


5'00 


5-05 


26 


4-61 


4-63 


4-65 


4-68 


4-71 


474 


4*77 


4-80 


4'83 


4'87 


4-91 


4*95 


4'99 


5'04 


5 '09 


27 


4'65 


4-67 


4-69 


4-72 


475 


4'78 


4-81 


4'8 4 


4-88 


4-91 


4*95 


5'oo 


5'04 


5'o8 


5'i3 


28 


4-69 


4-71 


474 


4-76 


479 


4-82 


4-85 


4-89 


4-92 


4-96 


5-00 


5*04 


5-08 


5'i3 


5'i8 


2Q 


4*73 


4-76 


4-78 


4-81 


4-84 


4-87 


4-90 


4'93 


4*97 


5'0i 


5'05 


5-09 


5-I3 


5'i8 


5'23 


30 


4'78 


4-80 


4-83 


4-86 


4-88 


4*92 


4'95 


4-98 


5'02 


5'o6 


5'io 


5'H 


5'i8 


5-23 


5-28 


31 


4-83 


4-85 


4-88 


4-91 


4'94 


4'97 


S'oo 


5'03 


5'7 


5'ii 


5'i5 


5-19 


5*24 


5'29 


5'34 


32 


4-88 


4-91 


4'93 


4-96 


4*99 


5'02 


5-05 


5-09 


5*12 


5'i6 


5'20 


5*25 


5*29 


5'34 


5'39 


33 


4'94 


4-96 


4*99 


5'0i 


5*04 


5'08 


5'ii 


5'i4 


5-i8 


5'22 


5-26 


5'3i 


5'35 


5'40 


5*45 


34 


5'oo 


5'02 


5'05 


5-07 


5'io 


5'i3 


5-I7 


5*20 


5-24 


5-28 


5*32 


5*37 


5*42 


5H6 


5'52 


35 


5-06 


5'o8 


S-" 


5*13 


5'i6 


5-20 


5-23 


5-27 


5*3<> 


5-35 


5*39 


5'43 


5-48 


5'53 


5'58 


36 


5'i2 


5'I4 


5*i7 


5*20 


5-23 


5'26 


5*30 


5*33 


5*37 


5'4i 


5'46 


5*50 


5'55 


5'6o 


5-65 


37 


5-I9 


5*21 


5*24 


5-27 


5-30 


5'33 


5-36 


5*40 


5*44 


5M8 


5'53 


5'57 


5'62 


5-67 


573 


38 


5-26 


5-28 


5'3* 


5'34 


5'37 


5HO 


5'44 


5'47 


5'5i 


5-56 


5'6o 


5'65 


57 


575 


5'8o 


39 


5'33 


5*35 


5-38 


5*4i 


5'44 


5-48 


5'5i 


5'55 


5'59 


5'6 3 


5'68 


573 


578 


5-83 


5-88 


40 


5HI 


5'43 


5-46 


5'49 


5-52 


5-56 


5*59 


5-63 


5-67 


572 


576 


5'8i 


5-86 


5*9i 


5'97 


4 1 


5'49 


5*51 


5'54 


5*57 


5-61 


5'6 4 


5-68 


572 


576 


5'8o 


5-85 


5-90 


5'95 


6-00 


6-06 


42 


5'57 


5-60 


5'63 


5-66 


5-69 


573 


5*77 


5'8i 


5'85 


5'89 


5'94 


5*99 


6-04 


6'io 


6-15 


43 


5*66 


5-69 


5'72 


5*75 


5-78 


5-82 


5'86 


5'90 


5'94 


5*99 


6-03 


6-09 


6-14 


6-19 


6-25 


44 


576 


5-78 


5'8i 


5-85 


5'88 


5-92 


5-96 


6-00 


6*04 


6*09 


6-14 


6*19 


6-24 


6-30 


6-36 


45 


5'86 


5-88 


5-92 


5'95 


5-98 


6*02 


6-06 


6'io 


6-15 


6*19 


6-24 


6-29 


6-35 


6-41 


6- 4 7 


46 


5'97 


5'99 


6'O2 


6-05 


6*09 


6-13 


6-17 


6-21 


6-26 


6-30 


6-35 


6-41 


6-46 


6-52 


6-58 


47 


6-07 


6'io 


6-13 


6-17 


6'2O 


6-24 


6-28 


6-33 


6-37 


6-42 


6- 4 7 


6-53 


6-58 


6-64 


671 


48 


6-19 


6-22 


6-25 


6-29 


6-32 


6-36 


6-40 


6-45 


6-49 


6'54 


6-60 


6-65 


671 


677 


6-83 


49 


6-31 


6-34 


6-38 


6-41 


6-45 


6-49 


6-53 


6-58 


6-62 


6-67 


673 


678 


6-84 


6-91 


6-97 


50 


6-44 


6-47 


6-51 


6-54 


6-58 


6-62 


6-67 


671 


6-76 


6'8i 


6-87 


6'92 


6-98 


7'5 


7-11 


51 


6-58 


6-61 


6-65 


6-68 


6-72 


6-76 


6-81 


6-86 


6-90 


6-96 


7-01 


7-07 


7'*3 


7-20 


7-27 


52 


6*73 


676 


6-79 


6-83 


6-87 


6'9i 


6-96 


7-01 


7-06 


7-11 


7-17 


7*23 


7-29 


7-36 


7'43 


53 


6-88 


6*91 


6'95 


6-99 


7*03 


7-07 


7-12 


7-17 


7-22 


7-28 


7'33 


7'39 


7'46 


7'53 


7-60 


54 


7'05 


7-08 


7-12 


7-16 


7*20 


7-24 


7'29 


7*34 


7*39 


7*45 


7'5i 


7'57 


7-64 


771 


7.78 


55 


7-22 


7*25 


7-29 


7*33 


7*38 


7-42 


7 '47 


7'52 


7-58 


7' 6 3 


7-69 


776 


7-83 


7-90 


7'97 


56 


7-41 


7'44 


7H8 


7*52 


7'57 


7-61 


7-66 


7-71 


777 


7-83 


7-89 


7-96 


8-03 


8*10 


8-18 


57 


7-60 


7-64 


7-68 


7-72 


7*77 


7-82 


7-8 7 


7-92 


7-98 


8-04 


8'io 


8-17 


8-24 


8-32 


8-40 


58 


7-81 


7-85 


7-89 


7*94 


7'98 


8-03 


8-09 


8-14 


8'20 


8-26 


8-33 


8-40 


8-47 


8-55 


8-63 


59 


8-04 


8-08 


8'12 


8-17 


8-21 


8-26 


8-32 


8-38 


8-44 


8-50 


8-57 


8-64 


872 


8'8o 


8-88 


60 


8-28 


8-32 


8-37 


8-41 


8-46 


8-51 


8-57 


8-63 


8-69 


876 


8-83 


8-90 


8-98 


9*06 


9'i5 



To convert time into longitude divide by 4. Thus 8-28 s. + 4 2-07' long. 



78 

Table D. 

SHOWING THE ERROR PRODUCED IN THE TIME OR LONGITUDE BY AM ERROR OF i' IN THE 

ALTITUDE. 



La*. 


AZIMUTHS. 


60 


59 


58 


57 


58 


55 


54 


58 


52 


51 


50 


49 


48 


47 


46 


o^ 


S. 


s. 


S. 


s. 


S. 


S. 


s. 


S. 


S. 


s. 


S. 


8. 


8. 


8. 


S. 


O 


4-62 


4-67 


472 


477 


4-82 


4-88 


4'94 


5-oi 


5'08 


5*15 


5'22 


5*30 


5*38 


5'47 


5'56 


I 


4-62 


4-67 


472 


477 


4-83 


4-88 


4*95 


5*oi 


5'o8 


5-15 


5'22 


5*30 


5-38 


5'47 


5-56 


2 


4-62 


4-67 


472 


477 


4-83 


4-89 


4'95 


5'oi 


5-08 


5-15 


5'22 


5'30 


5*39 


5*47 


5-56 


3 


4-63 


4-67 


472 


478 


4-83 


4-89 


4*95 


5'02 


5-o8 


5'i5 


5-23 


5-31 


5'39 


5-48 


5'57 


4 


4-63 


4-68 


473 


478 


4-84 


4-90 


4-96 


5-02 


5-09 


5'i6 


5-23 


5'3I 


5'40 


5H8 


5*57 


5 


4-64 


4-68 


473 


479 


4-84 


4-90 


4-96 


5-03 


5'io 


5*17 


5'24 


5'32 


5-40 


5*49 


5*58 


6 


4-64 


4-69 


474 


4-80 


4-85 


4-91 


4'97 


5*04 


5'io 


5-17 


5-25 


5*33 


5*4i 


5*50 


5*59 


7 


4-65 


47 


475 


4-81 


4-86 


4-92 


4-98 


S'OS 


5'n 


5*19 


5-26 


5*34 


5-42 


5'5i 


5'6o 


8 


4-66 


471 


476 


4-82 


4-87 


4'93 


4*99 


5-06 


5'i3 


5'20 


5-27 


5*35 


5'44 


5*52 


5-62 


9 


4-68 


472 


478 


4-83 


4-89 


4'94 


5'oi 


5*07 


5-I4 


5*21 


5-29 


5'37 


5*45 


5*54 


5'63 


10 


4-69 


474 


479 


4-84 


4-90 


4-96 


5'02 


5'09 


5-I5 


5*23 


5-30 


5-38 


5*47 


5*55 


5-65 


ii 


471 


475 


4-81 


4-86 


4-92 


4'97 


5*04 


5'io 


5-17 


5-24 


5*32 


5*40 


5'48 


5'57 


5'66 


12 


4-72 


477 


4-82 


4-88 


4*93 


4*99 


5'05 


5-12 


5'i9 


5-26 


5-34 


5*42 


5'50 


5'59 


5-68 


13 


4*74 


479 


4'8 4 


4-89 


4'95 


5*oi 


5*07 


5'i4 


5'2i 


5-28 


5-36 


5'44 


5-52 


5'6i 


57i 


14 


4-76 


4-81 


4-86 


4-92 


4'97 


5'03 


5'io 


5-i<3 


5-23 


5'3o 


5-38 


5-46 


5*55 


5-6 4 


573 


15 


4-78 


4-83 


4-88 


4'94 


5'oo 


5'o6 


5*12 


5-19 


5-26 


5'33 


5-41 


5'49 


5*57 


5-66 


576 


16 


4-80 


4'85 


4-91 


4-96 


5-02 


5'08 


S'M 


5*21 5-28 


5'35 


5-43 


5'5i 


5'6o 


5-69 


578 


17 


4-83 


4-88 


4*93 


4'99 


5'05 


5*n 


5*17 


5'24 5-3i 


5-38 


5-46 


5*54 


5-63 


572 


5'8i 


18 


4 -86 


4-91 


4-96 


5'0i 


5'07 


5-I3 


5'20 


5-27 


5'34 


5*4 J 


5-49 


5'57 


5-66 


575 


5-8 5 


Z 9 


4-88 


4*94 


4'99 


5*04 


5'io 


5-16 


5'23 


5'3o 


5'37 


5*44 


5-52 


5-60 


5'69 


578 


5-88 


20 


4-92 


4 - 97 


5'02 


5-08 


5'I3 


5'20 


5-26 


5'33 


5*40 


5M8 


5-56 


5*64 


573 


5-82 


5-92 


21 


4*95 


5-00 


5'05 


5-ii 


5*i7 


5'23 


5*30 


5-36 


5'44 


5'5i 


5'59 


5-68 


577 


5'86 


5-96 


22 


4'98 


5'03 


5 '09 


5'H 


5'20 


5'27 


5'33 


5MO 


5*47 


5*55 


5-63 


572 


5'8i 


5'90 


6'oo 


23 


5*02 


5*07 


5-12 


5'i8 


5*24 


5'3o 


5'37 


5*44 


5'5i 


5'59 


5-67 


576 


5-8 5 


5'94 


6-04 


24 


5'06 


5'H 


5'i6 


5'22 


5-28 


5'34 


5'4i 


5M8 


5-56 


5-63 


572 


5-80 


5-89 


5'99 


6-09 


25 


5-10 


5'i5 


5'2o 


5-26 


5-32 


5*39 


5M6 


5*53 


5-6o 


5-68 


576 


5-8 5 


5'94 


6-03 


6-13 


26 


5*H 


5-19 


5*25 


5'3i 


5'37 


5'43 


5-50 


5*57 


5'65 


573 


5'8i 


5-90 


5'99 


6-09 


6-19 


27 


5'i8 


5'24 


5-29 


5*35 


5'42 


5-48 


5'55 


5-62 


570 


578 


5-86 


5'95 


6-04 


6-14 


6-24 


28 


5'23 


5-28 


5'34 


5*40 


5-46 


5'53 


5'6o 


5-67 


575 


5'83 


5-91 


6-00 


6'io 


6-19 


6-30 


29 


5*28 


5'34 


5'39 


5*45 


5*52 


5-58 


5-65 


573 


5'8o 


5'88 


5*97 


6-06 


6-15 


6-25 


6-36 


3 


5'33 


5'39 


5'45 


5'5* 


5'57 


5-64 


571 


578 


5-86 


5*94 


6-03 


6-12 


6-22 


6-32 


6-42 


3 1 


5*39 


5'44 


5*50 


5-56 


5*63 


57 


577 


5-84 


5'92 


6-00 


6-09 


6-18 


6-28 


6-38 


6-49 


3 2 


5'45 


5*50 


5-56 


5-62 


5-69 


576 


5-83 


5-9i 


5'99 


6*07 


6-16 


6-25 


6-35 


6-45 


6-56 


33 


5'5* 


5-56 


5-62 


5-69 


575 


5-82 


5'9o 


5'97 


6-05 


6-14 


6-23 


6-32 


6-42 


6-52 


6-63 


34 


5*57 


5*63 


5'69 


575 


5-82 


5'89 


5'96 


6-04 


6-12 


6-21 


6-30 


6-39 


6-49 


6-60 


6-71 


35 


5-64 


570 


576 


5-82 


5*89 


5-96 


6-04 


6-n 


6'2O 


6-28 


6-37 


6-47 


6-57 


6-68 


679 


36 


5*7i 


577 


5-83 


5-90 


5-96 


6*04 


6-n 


6-19 


6-27 


6-36 


6'45 


6-55 


6-65 


6-76 


6-87 


37 


578 


5-84 


5*91 


5'97 


6*04 


6-n 


6*19 


6-27 


6-36 


6-44 


6'54 


6-64 


674 


6-85 


6-96 


38 


5'86 


5*92 


5'99 


6-05 


6-12 


6-20 


6-27 


6-36 


6-44 


6-53 


6-63 


673 


6-83 


6-94 


7-06 


39 


5'94 


6 'oo 


6-07 


6-14 


6-21 


6-28 


6-36 


6-44 


6-53 


6-62 


672 


6-82 


6'93 


7-04 


7-16 


40 


6-03 


6-09 


6-16 


6-23 


6-30 


6-37 


6-45 


6-54 


6-63 


672 


6-82 


6-92 


7'03 


7-14 


7-26 


4 1 


6-12 


6-18 


6-25 


6-32 


6-39 


6-47 


6-55 


6-64 


673 


6-82 


6-92 


7-02 


7'i3 


7*25 


7'37 


42 


6-22 


6-28 


6-35 


6-42 


6-49 


6-57 


6-65 


674 


6-83 


6*93 


7-03 


7'i3 


7-24 


7-36 


7-48 


43 


6-32 


6-38 


6- 4 5 


6-52 


6-60 


6-68 


676 


6-85 


6-94 


7-04 


7-14 


7'25 


7-36 


7-48 


7-60 


44 


6-42 


6-49 


6-56 


6-63 


671 


679 


6-87 


6-96 


7-06 


7-16 


7-26 


7'37 


7M8 


7-60 


773 


45 


6-53 


6-60 


6-67 


675 


6-82 


6-91 


6-99 


7-08 


7-18 


7-28 


7-38 


7-5 


7-61 


773 


7-86 


46 


6-65 


672 


679 


6-87 


6'95 


7*03 


7-12 


7-21 


7'3i 


7-41 


7'52 


7-63 


775 


7-87 


8-00 


47 


6-77 


6-84 


6-92 


6-99 


7-07 


7-16 


7-25 


7'34 


7'44 


7'55 


7-66 


777 


7-89 


8-02 


8-15 


48 


6-90 


6-97 


7'5 


7'*3 


7-21 


7'30 


7'39 


7'49 


7'59 


7-69 


7-80 


7*92 


8-04 


8-17 


8-31 


49 


7-04 


7-11 


7-19 


7-27 


7*35 


7'44 


7'54 


7-63 


774 


7-85 


7-96 


8-08 


&-20 


8-34 


8-48 


5<> 


7-19 


7-26 


7'34 


7*42 


7*5i 


7-60 


7-69 


779 


7-90 


8-oi 


8-12 


8-25 


8-37 


8-51 


8-65 


51 


7*34 


7-42 


7*49 


7-58 


7-67 


776 


7-86 


7-96 


8-07 


8-18 


8-30 


8-42 


8-55 


8-69 


8-84 


52 


7'5o 


7-58 


7-66 


775 


7-84 


7'93 


8-03 


8-14 


8-24 


8-36 


8-48 


8-61 


874 


8-88 


9-03 


53 


7-67 


775 


7-84 


7'93 


8-02 


8-n 


8'22 


8-32 


8-43 


8'55 


8-68 


8-81 


8-94 


9-09 


9-24 


54 


7-86 


7 '94 


8-02 


8-n 


8-21 


S'3i 


8- 4 I 


8-52 


8-64 


876 


8-88 


9-02 


9*16 


9*3 


9-46 


55 


8-05 


8-14 


8-22 


8-32 


8-41 


8-51 


8-62 


873 


8-85 


8-97 


9-10 


9-24 


9'38 


9'54 


9-69 


56 


8-26 


8'35 


8-43 


8'53 


8-63 


873 


8-84 


8-96 


9-08 


9'2O 


9'34 


9-48 


9-63 


978 


9*94 


57 


8-48 


8-57 


8-66 


876 


8-86 


8'97 


9'08 


9*20 


9'32 


9-45 


9'59 


973 


9-88 


10-04 


IO-2I 


58 


8-72 


8-81 


8-90 


9*00 


9-10 


9-21 


9'33 


9*45 


9-58 


971 


9-85 


lO'OO 


10-16 


10-32 


10-49 


59 


8-97 


9-06 


9-16 


9-26 


9'37 


9-48 


9-60 


972 


9-86 


9-99 


10-14 


10-29 


10-45 


10-62 


10-80 


60 


9-24 


9'33 


9'43 


9'54 


9-65 


977 


9-89 


10-02 


10-15 


IO'29 


10-44 


10-60 


10-77 


10-94 


II'I2 



To convert time Into longitude divide by 4. Thus 9-243. 4- 4 2-31' lon^. 



79 



Table D. 

SHOWING THE ERROR PRODUCED IN THE TIME OR LONGITUDE BY AN ERROR OF i' IN 

ALTITUDE. 





AZIMUTHS. 




45 44 


43' 


42 


41 C 


40 


39 


38" 37 C 36 


35 


34 


33 


32 


31 





S. j S. 


S. 


S. 


S. 


s. 


S. 


S. 


s. 


s. 


S. 


s. 


S. 


S 


S. 





5*66; 57' 


5*8; 


J 5*9 


6-10 


6-2- 


i 6-3 


6' 5 < 


3 6-6 


6-8 


6-9' 


1 7' 


7*3 


7*5 


777 


I 


5'66j 57' 


5*8: 


' 5*9< 


6-10 


6-2: 


i 6-3 


6- 5 < 


3 6-6 


6-8 


6- 9 ' 


7 7* 


7*3 


7*5 


777 


2 

3 


5*6f 

5 -6e 


> 57< 
57; 


5'8; 
5*8; 


* 5*9* 
' 5'9< 


6-10 
6-n 


6-23! 6-3 
6-23 6-3 


6'5< 
6'5 


3 6-6 
6-6< 


6-8 
6-8 


6-9? 
6-9* 


* 7* 
5 7- ( 


7'3. 
7'3. 


7*5 
7*5 


* / / 

777 j 
7-78 


4 


5'6/ 


5*7^ 


5*8* 


* 5*9< 


6-u 


6-2, 


^ 6-3 


6-5 


6-6( 


6-8 


6- 9 c 


) T ' 


7'3< 


7*5 


779 


5 


5*6 


5*7* 


5*8c 


6-oc 


6-12 


6'2j 


> 6-3 


6-5: 


> 6-6' 


6-83 


7-oc 


) 7* * 


7'33 


7*5 


7-80 


6 


5'6s 


57 C 


5'9c 


6-0] 


6-13 


6'2( 


6'3c 


6-5: 


\ 6-6! 


6-84 


7-0] 


7-ic 


7*3* 


7*5 


7-81 


7 


5'7 C 


5'8c 


5*91 


6-oi 


6-14 


6-27 


6- 4 c 




6-7C 


6-86 


7-05 


1 7-2 


7- 4 c 


7-6 


782 


8 


5-7 1 


5*81 


5*92 


6*0^ 


6-16 


6-2* 


6-42 


6-5< 


6- 7 ] 


6-87 




7-22 


7-42 


7-6 


7'84 


9 


5*73 


5*83 


5*9^ 


6-0= 


6-17 


6-30 


6-44 


6-5* 


6-7; 


6-89 


7-oe 


7*2^ 


7'44 


7-6 


7-86 


10 


5*74 


5*85 


5-96 


6-07 


6-19 


6-32 


6-45 


6-6c 


6*7* 


6-91 


7-oS 


7-2t 


7-46 


7-6 


789! 


ii 


5*76 


5-87 


5*97 


6-oc 


6-21 


6-34 


6-48 


6-62 


6-77 


6-93 


7-ic 




7-48 


7-6 


7-91 1 


12 


5*78 


5'8c 


6-00 


6-n 


6-23 


6-36 


6-50 


6-64 


6-8c 


6-96 


7*13 


73 


7 5i 


7 7 


7'94I 


13 


5*8i 


5-91 


6-02 


6-14 


6-26 


6-39 


6-52 


6-67 


6-82 


6-98 


7-16 


7'3< 


7"54 


77 


7 971 


14 


5*83 


5*93 


6-04 


6-16 


6-28 


6-41 


6-55 


6-70 


6-85 


7-01 


7-19 


7 3" 


7 57 


7 7 


8oo\ 


15 


5*86 


5*96 


6-07 


6-ig 


6-31 


6-44 


6-58 


6*73 


6-88 


7*05 


7-22 


7-41 


7'6o 


7-8 


8*04 [ 


16 


5-88 


5*99 


6-10 


6-22 


6-34 


6-47 


6-61 


6-76 


6-91 


7-08 


7*25 


7*44 


764 


785 


8 08 I 


17 


5'9 2 


6'O2 


6-13 


6-25 


6-38 


6-51 


6-65 


6-79 


6-95 


7-12 


7*29 


7-48 


768 


7-89 


8 12 I 


18 


5*95 


6*05 


6-17 


6-28 


6-41 


6-54 


6-68 


6-83 


6-99 


7*16 


7*33 


7*52 


7 72 


7 94 


817! 


19 


5-98 


6-09 


6-20 


6-32 


6-45 


6-58 


6-72 


6-87 


7'3 


7-20 




7'57 


7 77 


7-98 


Sail 


20 


6*O2 


6-13 


6-24 


6-36 


6-49 


6-62 


6-76 


6-91 


7-07 


7*24 


7-42 


7-61 


7-82 


803 


8*261 


21 


6-06 


6-17 


6-28 


6-40 


6'53 


6-67 


6-81 


6-96 


7-12 


7*29 


7*47 


7-66 


7-87 


8-09 


8 32 1 


22 


6-10 


6-21 


6*33 


6*45 


6-58 


6-71 


6-86 


7-01 


7-17 


7'34 


7*52 77i 


7*92 


8-14 


8-38 


23 


6-15 


6-26 


6* 37 


6-49 


6-62 


6-76 


6-90 


7-06 


722 


7'39 


7-58 


777 


7-98 


8-20 


8-44 


24 


6-19 


6-30 


6-42 


6-54 1 6-67 


6-81 


6-96 


7-11 


7-28 


7'45 


7*63 




8-c 4 


8-26 


850 


25 


6-24 


6-35 


6-47 


6-60 


6-73 


6-87 


7-01 


7-17 


7'33 




7-69 


7-89 


8-10 


8*33 


857 


26 


6-29 


6-41 


6*53 


6-65 


6-78 


6-92 


7*07 


7*23 


7*39 


7*57 


7*76 


7-96 


8-17 


8-40 


8-64 j 


27 


6-35 


6-46 


6-58 


6-71 


6-84 


6-98 


7*i3 


7*29 7*46 


7-64 


7*83 


8-03 


8-24 


8-47 


872 


28 


6-41 


6-52 


6-64 


6-77 


6-gi 


7*05 


7-20 


7*36 7'53 


7-7i 


7-90 


8-10 


8-32 


8-55 


8*80 I 


29 


6-47 


6-58 


6- 7I 


6-83 6-97 


7-11 


7-27 


7*43 7*6o| 778 


7 '97 


8-18 


8-40 


8-63 


8-881 


30 


6*53 


6-65 


6-77 


6-90! 7-04 


7-19 


7*34 


7-50 7-67 


7-86 


8-05 


8-26 


8-48 


8*72 


897 


31 


6-60 


6-72 


6-84 


6-97 


7-11 


7-26 


7*42 


7-58 


7*75 


7*94 


8-14 


8*35 


8-57 


8-81 


9-06 


32 


6-67 


679 


6-92 




7-19 


7*34 


7*49 


7-66 


7*84 


8 02 


8-22 


8*43 


8-66 


8-90 


9-16 


33 


6-74 


6-87 


6-99 7-13 


7*27 


7-42 




775! 7*93 


8"ii 


8-32 


8*53 


8-76 


9-00 


926 


34 


6-82 


6*95 


7*07 


7-21 


7*35 




7-67 


7-84 8-02 


8-21 


8-41 


8-63 


8-86 


9-10 


9*37 [ 


35 


6-91 


7*03 


7-16 




7'44 


7-60 


7-76 


7'93 


8-n 


8-31 




8*73 


8-97 


9-21 


9 48 I 


36 


6-99 


7-12 


7*25 


7'39 


7*54 


7-69 


7-86 


8-03 


8-22 


8-41 


8-62 


8-84 


9-08 


9*33 


9-60 I 


37 


7-08 


7-21 


7*34 


7*49 


7*63 


779 


7-96 


8-14 


8- 3 2 


8-52 


8*73 


8-96 


9-20 


9*45 


9-721 


38 


7-18 


7*3i 


7'44 


7*59 


7*74 


7-90 


8-07 


8-24 


8*43 


8-64 


8-85 


9-08 


9*32 


9*58 


9-861 


39 


7-28 


7-41 


7'55 


7-69 


7*85 


8-01 


8-18 


8-36 


8*55 


8-76 


8-97 


9-20 


9*45 


9-71 


9-991 


40 


7-38 


7*52 


7*66 


7-80 


7*96 


8-12 


8-30 


8-48 


8-68 


8-88 


9-10! 9-34 


9-59 


9-85 


0-14 I 


41 


7*50 


7-63 


7*77 


7*92 


8-08 


8-25 


8-42 


8-61 


8-81 


9-02 


9-24 


9*48 


9*73 


10-00 


0-291 


42 


7-61 


775 


7-89 


8-04 


8-20 


8*37 


8-55 


8-74 


8*94 


9-16 


9*38 


9-63 


9-88 


10-16 


0'45 I 


43 


7*73 


7*87 


8-02 


8-17 


8-34 




8-69 


8-88 


9*09 


9*30 


9*54 


9-78 


10-04 


10-32 


0-62! 


44 


7-86 


8-00 


8-15 


8-31 


8-48 


8-65 


8-84 


9*3 


9*24 


9-46 


9-69 


9*94 


IO'2I 


10-49 


0-80 1 


45 


8-00 


8-14 


8-29 


8*45 


8-62 


8-80 


8-99 


9-19 


9*4 


9-62 


9-86 


10*12 


10-39 


10-67 


0-98 | 


46 


8-14 


8-29 


8*44 


8-61 


8-78 


8-96 


9*15 


9*35 


9*57 


9-80 


0-04 


10-30 


10-57 


10-87 


i i8l 


47 


8-29 


8-44 


8-60 


8-77 


8*94 


9-12 


9*32 


9*53 


9*75 


9-98 


0-23 


10-49 


1077 


11-07 


i 39 I 


48 


8-45 


8-61 


8*77 


8*93 


9-11 


9*30 


9*50 


9-71 


9*93 


10-17 


0-421 10-69 


10-97 


11-25 


1-61 I 


49 


8-62 


8-78 


8-94 


9-11 


9-29 


9*49 


9-69 


9*90 


10-13 


10-37 


0-631 10*90 


11-19 


11*51 


i -84 j 


50 


8-80 


8-96 


9-12 


9*30 


9*49 


9-68 


9-89 


10-11 


10-34 


10-59 


0-851 "'13 


ii*43 


11-74 


2-08 I 


5I 


8*99 


9"i5 


9*32 


9*50 


9-69 


9-89 


lO'IO 


10-30 


10-56 


10-81 


1-081 11-37 


11-67 


11-99 


234J 


52 


9-19 


9*35 


9*53 


9-71 


9*90 


O'll 


10-32 


10-55 


10-80 


11-05 


1-33 


11-62 


11-93 


12-26 


2*61 1 


53 


9*4 


9*57 


9*75 


9*93 


10-13 


o*34 


10-56 


10-80 


11-04 


11-31 


i"59 


11-89 


I2'2O 


12-54 


2-90 1 


54 


9-62 


9-80 


9-98 


10-17 


10-37 


*59 


10-81 


11-05 


11-31 


11-58 


1-86 


12-17 


12*50 


12-84 


3-21 1 


55 


9-86 


10-04 


10-23 


10-42 


10-63 


0-85 


1 1 -08 


n-33 


ii*59 


11-86 


2-16 


12-47 


12-80 


13-16 


354| 


56 


IO'I2 


10-30 


10-49 


10-69 


10-90 


1-13 


ii*37 


11-62 


11-89 


12-17 


2*47 


12-79 


I3*I3 


13*50 


389! 


57 


10*39 


10-57 


1077 


10-97 


11-19 


i*43 


11-67 


11-92 


I2'2O 


12-49 


2-80 


I 3' I 3 


I3'48 


13*86 


14*26 I 


58 


10-67 


10-87 


11-07 


11-28 


11-51 


1-74 


11-99 


12-26 


12-54 


12-84 


3-16 


13*5 


13-86 


14*24 


14*66 


59 


10*98 


ii'iB 


11-39 


11-61 


11-84 


2-08 


12-34 


12-61 


12-90 


13*21 


3*54 


13-89 


14-26 


14-66 


I5*o81 


60 


II- 3 I 


11-52 


"*73 


11-96 


12-19 


2-45 


12-71 


12-99 


13-29 


13-61 


3'95 


I43I 


14-69 


15-10 


15*53 1 



To convert time into longitude divide by 4. Thus 12-0 s. -=- 4 3' long. 



80 



Table D. 

SHOWING THE ERROR PRODUCED IN THE TIME OR LONGITUDE BY AN ERROR OF i' IN THB 

ALTlTUbE. 



T ~4 


AZIMUTHS. 


Lifts. 


30 


29 


23 27 


26 


25 


24 


23 


22 n 2F 


2(P . 19 3 18 ! 17 


16^ 


















1 


I 







S. 


S. 


S. 


s. s. 


3. : S. 


s. s. 


s. 


S. 


S. 


s. s. 


S. 


O 


8-00 


8-25 


8-52 


8-81 


9-12 


9-46! 9-83 


IO'2 


107 


II'2 


II'7 


12-3 


13-0 


137 


I 4'5 


I 


8-00 


8-25 


8-52 


8-81 


9'13 


9'47 


9'8 4 


I0'2 


107 


II'2 


II'7 


12-3 


13-0 


137 


H'5 


2 


8-00 


8-26 


8-53 


8-82 


9-13 


9*47 


9-84 


IO'2 


I0'7 


II'2 


117 


12-3 


13-0 


137 


14*5 


3 


8-01 


8-26 


8'53 


8-82! 9-14 


9-48 


9-85 


I0'3 


I0'7 


11*2 


II'7 


12-3 


13-0 


137 


H'5 


4 


8-02 


8-27 


8-54 


8-83 9-15 


9'49 


9'86 


10-3 


I0'7 


II'2 


II'7 


I2' 3 


13-0 


137 


i4'5 


5 


8-03 


8-28 


8-55 


8-84 9-16 


9'50 


9-87 


10-3 


107 


II'2 


II'7 


12-3 


13-0 


137 


14-6 


6 


8-04 


8-30 


8-57 


8-86 9-17 


9'52 


9-89 


10-3 


107 


II'2 


ii-8 


12-4 


13-0 


13-8 


14-6 


7 


8-06 


8-31 


8-58 


8-88! 9-19 


9'54 


9-91 


10-3 


io-8 


II'2 


ii-8 


I2' 4 


13-0 


13-8 


i 4 -6 


8 


8-08 


8-33 


8-60 


8-90 9-21 


9'56| 9'93 


10-3 


lo-S 


1 1 '3 


ii-S 


12-4 


13-1 


13-8 


147 


9 


S'io 


8-35 


8-63! 8-92! 9-24 


9'58 


9-96 


10-4 


10-8 11-3 


ii'8 12-4 


13-1 


13*9 


H7 


10 


8-12 


8-38 


8-65 


8-95 9-27 


9-61 


9-99 


10-4 


10-8 


11-3 


11-9 


12-5 


13-1 


13-9 


147 


n 


8-15 


8-41 


8-68 


8-98! 9-30 


9-64 


lO'O 


10-4 


io'9 


11-4 


11-9 


12-5 


13-2 


13*9 


I 4 '8 


12 


8-18 


8- 4 3 


8-71 


9-oii 9-33 


9-68 


lO'I 


10-5 


io'9 


11-4 


I2'O 


I2'6 


13-2 


I 4 '0 


I 4 '8 


13 


8-21 


8-47 


8-74 


9-04 9-36 


971 


lO'I 


10-5 


ii'O ii'5 


I2'0 


I2'6 


*3'3 


I 4 '0 


i 4 '9 


H 


8-24 


8-50 


8-78 


9-08! 9-40 


9'75 


lO'I 


10-6 


II'O 


"'5 


I2'I 


127 


13-3 


I 4 'I 


15-0 


15 


8-28 


8-54 


8-82 


9-12 


9'45 


9-80 


10'2 


10-6 


ii'i 


ii-6 


I2'I 


127 


J 3'4 


I 4 '2 


15-0 


16 


8-32 


8-58 


8-86 


9-17 


9'49 


9-85 


I0'2 


io'6 


ii'i 


ii'6 


I2'2 


I2'8 


i3'5 


I 4 '2 


i5'i 


i? 


8-37 


8-63 


8-91 


9-21 


9'54 


9-90 10-3 


107 


II'2 


117 


I2'2 


12'8 


i3'5 


14*3 


15-2 


18 


8-41 


8-68 


8-96 


9-26 


9' 59 


9'95 10-3 


10-8 


II'2 


117 


12-3 


12-9 


13-6 


14-4 


I5'3 


19 


8- 4 6 


8-73 


9-01 


9-32 


9'65 


lo-o j io'4 


10-8 


ii'3 


ii-8 


12-4 


13-0 


137 


J 4'5 


I5-3 


20 


8-51 


8-78 


9-07 


9-38 


971 


io'i 10-5 


10-9 


11-4 


11-9 


I2' 4 


13-1 


13-8 


14-6 


I5'4 


21 


8'57 


8-84 


9-13 


9'44! 977 


IO'I 


10-5 


II'O 


11-4 


I2'0 


12-5 


13-2 


I3-9 


147 


I5'5 


22 


8-63 


8-90 


9-19 


9-50 9-84 


I0'2 


10-6 


II'O 


n'5 


I2'0 


I2'6 


13-3 


I 4 '0 


14-8 


157 


23 


8-69 


8-96 


9/26 9-57 


9-91 


10-3 


107 


II'I 


11-6 


I2'I 


127 


13-3 


14-1 


14-9 


I 5 '8 


24 


8-76 


9-03 


9'33 9-64 


9*99 


10-4 


10-8 


II-2 


117 


I2'2 


I2'8 


13-4 


14-2 


15-0 


I5'9 


25 


8-83 


9-10 


9-40 9-72 


lO'I 


10-4 


10-9 


"'3 


ii-8 


12-3 


12*9 


13-6 


14*3 


I5'i 


i6'o 


26 


8-90 


9-18 


9-48 9-80 


I0'2 


10-5 


io'9 


11-4 


11-9 


12-4 


13-0 


137 


14-4 


15-2 


16-1 


27 


8-98 


9-26 


9-56] 9-89 


IO'2 


10-6 


II'O 


'5 


I2'0 


12-5 


13-1 


13-8 


14*5 


I5'3 


16-3 


28 


9*06 


9' 34 


9-65 9-98 


I0'3 


107 


ii'i 


ii-6 


I2'I 


I2'6 


13-2 


13-9 


147 


I5-5 


i6' 4 


29 


9'i5 


9'43 


9-74 io'i 


io' 4 


10-8 


II'2 


117 


I2'2 


I2'8 


13*4 


14-0 


I4'8 


15-6 


16-6 


3 


9-24 


9'53 


9-84; IO'2 


10-5 


10-9 


ii' 4 


irS 


12-3 


12-9 


i3'5 


14-2 


14-9 


15-8 


16-8 


















i 














3 1 


9'33 


9-63 


9'94 


10-3 


io'6 


II'O 


ii*5 


11-9 


12-5 


13-0 


13-6 


14-3 


15-1 


i6'O 


16-9 


32 


9'43 


9'73 


lO'O 


10-4 


10-8 


II'2 


ii-e 


I2'I 


I2'6 


13-2 


i3'8 


14*5 


15-3 


16-1 


17-1 


33 


9'54 


9-84 


IO'2 


10-5 


10-9 


*3 


117 


I2'2 


127 


I3'3 


14-0 


14-6 


I5H 


16-3 


i7'3 


34 


9-65 


9'95 


IO- 3 


io'6 


II'O 


11-4 


1 1 -9 


11*3 


12-9 


i3'5 


14-1 


14-8 


i5'6 


16-5 


i7'5 


35 


977 


10' I 


IO- 4 


10-8 


ii'i 


n-6 


I2'0 


12-5 


13-0 


13-6 


i4'3 


15-0 


15-8 


167 


177 


36 


9-89 


10-2 


io'5 


10*9 


n'3 


117 


I2'2 


127 


13-2 


13-8 


M'5 


15-2 


i6'o 


i6'9 


17-9 


37 


lO'O 


I0'3 


10-7 


II'O 


11-4 


ii'9 12-3 j 12-8 


!3'4 


14-0 


14-6 


15-4 


16-2 


17-1 


18-2 


38 


IO'2 


10-5 


10-8 


II'2 


u-6 


I2'0 


12-5 


J 3 '0 


13-6 


14-2 


! 4 '8 


15-6 


16-4 


17-4 


i8' 4 


39 


10-3 


io-6 


II'O 


ii'3 


117 


I2'2 


127 


13-2 


137 


14-4 


15-0 


15-8 


167 


17-6 


18-7 


40 


10-4 


10-8 


II'I 


11-5 


11-9 


I2'4 


I2'8 


I3H 


*3'9 


! 4 '6 


^5*3 


:6-o 


16-9 


17-9 


18-9 


4 1 


io'6 


10-9 


ii'3 


117 


I2'I 


12-5 


I3'0 


i3'6 


14-1 


14-8 


15*5 


16-3 


17-2 


18-1 


19-2 


42 


10-8 


ii-i 


11-5 


11-9 


I2'3 


I2'7 


I3 f 2 


13-8 


14-4 


15-0 


157 16-5 


!7'4 


18-4 


I9-5 


43 


10-9 


11-3 


n-6 


I2'0 I2'5 


I2'9 


J3'4 


14-0 


14-6 


15-3 


16-0 16-8 


177 


187 


19-8 


44 


ii'i 


11-5 


ii-8 


I2'2 


127 


I3'2 


137 


14-2 


14-8 


I5'5 


16-3 


17-1 


18-0 


19-0 


2O'2 


45 


"'3 


11-7 


I2'O 


I2'5 


12-9 


I3H 


13*9 


H'5 


15-1 


i5'8 


16-5 


17-4 


18-3 


i9'3 


20'5 


46 


n*5 


11-9 


I2'3 


127 


I 3 -I 


I3'6 


14-2 


147 


I5-4 


16-1 


16-8 


177 


18-6 


197 


2O'9 


47 


11-7 


I2'I 


12-5 


I2'9 


I3'4 


I3-9 


14-4 


15-0 


157 


l6- 4 


17-1 


18-0 


19-0 


20'I 


21-3 


48 


I2'0 


12-3 


127 


13*2 


13-6 


I 4 'I 


147 


i5'3 


i6'O 


167 


I7'5 


18-4 


I9'3 


20'4 


217 


49 


I2'2 


I2'6 


.13*0 


i3'4 


13*9 


14-4 


15*0 


i5'6 


16-3 


17-0 


17-8 


187 


197 


20'9 


22'I 


50 


I2- 4 


12-8 


13*3 


13*7 


14-2 


I 4 7 


I5'3 


i5'9 


16-6 


17-4 


18-2 


19-1 


20' I 


21'3 


22'6 


5i 


I2'7 


13-1 


13*5 


14-0 


H'5 


I5'0 


I5'6 


16-3 


17-0 


177 


18-6 


J9'5 


2O'6 


217 


2 3 -I 


52 


I 3 -0 


13-4 


13-8 


i4'3 


14-8 


I5H 


i6'O 


16-6 


i7'3 


18-1 


19-0 


20'0 


2I'O 


22'2 


23-6 


53 


13*3 


137 


I 4 -2 


I4'6 


15*2 


15*7 


16-3 


17-0 


177 


18-5 


19-4 


20-4 


21-5 


227 


2 4 'I 


54 


13-6 


14-0 


H'5 


15-0 


I5-5 


16-1 


167 


17-4 


18-2 


19-0 


19-9 


20'9 


22'O 


23*3 


2 4 '7 


55 


i3'9 


14-4 


I4-9 


I5'4 


I5'9 


16-5 


17-1 


17-8 


18-6 


I9'5 


20-4 


21'4 


22'6 


23-9 


25^ 


56 


i4*3 


14-8 


I5'2 


15-8 


16-3 


i6'9 


17-6 


18-3 


19-1 


20'0 


20*9 


22'O 


2 3 'I 


24'5 


26'0 


57 


14-9 


I5'i 


15-6 


16-2 


16-8 


17-4 


18-1 


18-8 


19*6 


20' 5 


21-5 


22'6 


23-8 


25-1 


26' 4 


58 


15*1 


I5'6 


16-1 


16-6 


17-2 


17-9 


18-6 


I9'3 


20* i 


2I'I 


22'I 


23-2 


24*4 


25-8 


27-4 


59 


15*5 


i6'o 


16-5 


17-1 


177 


18-4 


19-1 


19-9 


207 


21'7 


22'7 


23*9 


25'2 


26-6 


28'2 


60 


16*0 


16-5 


17-0 


17-6 


18-2 


iS'g 


197 


20-5 


21-4 


22'3 


23-4 


2 4 '6 


25'9 


27-4 


29-0 



To convert time into longitude divide by 4. Thus i6s. -7-4=4' long. 



81 



Table D. 

SHOWING THE ERROR PRODUCED IN THE TIME OR LONGITUDE BY AN EKROR OF i' IN THE 

ALTITUDE. 



Lat. 


AZIMUTHS. 


15 


14 


13 


11 


11 


10 


9 3 


7 


6 


5 


4 


3 


2 


1 


o 


S. 


S. 


S. 


s. 


s. 


s. 


S. 


s. 


S. 


S. 


S. 


S. 


s. 


S. 


S. 





I5H 


I6'5 


I 7 -8 


19-2 


21-0 


23-0 


25-6 


28-7 


32-8 


38-3 


45'9 


57'4 


76-4 


"5 


229 


I 


I5'5 


I6'5 


I 7 -8 


i9'3 


21'0 


23-0 


25-6 


28-7 


32-8 


38-3 


45'9 


57-4 


76-4 


"5 


229 


2 


I5'5 


l6- 5 


17-8 


19*3 


21-0 


23-0 


25-6 


28-8 


32-8 


38-3 


45'9 


57'4 


76-5 


"5 


229 


3 


*5-5 


16-6 


I 7 -8 


i9'3 


21'0 


23-1 


25-6 


28-8 


32-9 


38-3 


46-0 


57'4 


76-5 


115 


230 


4 


15*5 


16-6 


I 7 '8 


i9'3 


21'0 


23-1 


25-6 


28-8 


32-9 


38-4 


46-0 


57*5 


76-6 


"5 


230 


5 


15-5 


16-6 


I 7 '8 


19*3 


21'0 


23-1 


257 


28-9 


32-9 


38-4 


46-1 


57-6 


76-7 


"5 


230 


6 


i5'5 


16-6 


17-9 


I9-3 


2I'I 


23-2 


257 


28-9 


33'o 


38-5 


46-1 


57'7 


76-9 


US 


230 


7 


15-6 


16-7 


17-9 


19-4 


21*1 


23-2 


25-8 


29-0 


33' 1 


38-6 


46-2 


57-8 


77' 


115 


231 


8 


15-6 


16-7 


18-0 


19-4 


21'2 


23-3 


25-8 


29-0 


33'i 


38-6 


46-3 


57'9 


77'2 


116 


231 


9 


15-6 


16-7 


18-0 


I9'5 


21'2 


23-3 


25*9 


29-1 


33'2 


38-7 


46-5 


58-1 


77'4 


116 


232 


10 


157 


16-8 


18-1 


I9-5 


21-3 


23-4 


26-0 


29-2 


33'3 


38-9 


46-6 


58-2 


77-6 


116 


233 


n 


i5'7 


16-8 


18-1 


19-6 


21'4 


23-5 


26-0 


29-3 


33'4 


39-0 


46-8 


58-4 


77'9 


117 


233 


12 


15-8 


16-9 


18-2 


i9'7 


2I- 4 


23-5 


26-1 


29-4 


33-6 


39'i 


46-9 


58-6 


78-1 


117 


234 


13 


i5'9 


17-0 


18-2 


19-7 


21'5 


23-6 


26-2 


29'5 


33'7 


39'3 


47-1 


58-9 


78-4 


118 


235 


M 


i5'9 


17-0 


i8'3 


19-8 


21-6 


23-7 


26-4 


29-6 


33-8 


39'4 


47'3 


59'i 


78-8 


118 


236 


15 


16-0 


17-1 


18-4 


19-9 


21-7 


23-8 


26-5 


29-8 


34'o 


39'6 


47*5 


59'4 


79-1 


119 


237 


16 


16-1 


17-2 


18-5 


20'0 


21-8 


24-0 


26-6 


29-9 


34'i 


39'8 


47T 


59'7 


79'5 


119 


238 


i? 


16-2 


i?'3 


18-6 


20*1 


21-9 


24-1 


26-7 


30-1 


34'3 


40-0 


48-0 


60-0 


79-9 


I2O 


240 


18 


16-2 


17-4 


18-7 


20'2 


22'O 


24-2 


26-9 


30-2 


34'5 


40-2 


48-3 


60-3 


8o- 4 


121 


.241 


19 


16-3 


i7'5 


18-8 


20'3 


22'2 


24-4 


27-0 


30-4 


34'7 


40-5 


48-5 


60-6 


80-8 


121 


242 


20 


16-4 


17-6 


18-9 


20'5 


22'3 


24-5 


27-2 


30*6 


34'9 


40-7 


48-8 


6i'o 


8!- 3 


122 


244 


21 


16-6 


17-7 


ig'-o 


2O'6 


22'5 


24*7 


27-4 


30-8 


35'2 


41-0 


49-2 


61*4 


81-9 


123 


246 


22 


16-7 


17-8 


19-2 


20-7 


22-6 


24-8 


27-6 


31-0 


35'4 


4 J '3 


49'5 


61-8 


82-4 


124 


247 


23 


16-8 


18-0 


i9'3 


20-9 


22-8 


25-0 


27-8 


31-2 


35'7 


41-6 


49'9 


62-3 


83-0 


125 


249 


2 4 


16-9 


18-1 


I9-5 


2I'I 


22'9 


25-2 


28-0 


31-5 


35'9 


41-9 


50-2 


62-8 


83-7 


125 


251 


25 


17-1 


18-2 


19-6 


21'2 


23T 


25-4 


28-2 


3I-7 


36-2 


42-2 


50-6 


63-3 


84-3 


126 


253 


26 


17-2 


18-4 


19-8 


21'4 


23-3 


25-6 


28-4 


32-0 


36-5 


42-6 


51*1 


63-8 


85-0 


128 


255 


27 


I7-3 


18-6 


2O'O 


21-6 


23'5 


25-8 


28-7 


32-3 


36-8 


42-9 


5!'5 


64-4 


85-8 


129 


257 


28 


17-5 


18-7 


20'I 


21-8 


237 


26-1 


29*0 


32-6 


37'2 


43'3 


52*0 


64-9 


86-6 


I 3 


260 


2Q 


17-7 


18-9 


20-3 


22'O 


24*0 


26-3 


29-2 


32-9 


37'5 


43-8 


52-5 


65-6 


87'4 


I3 r 


262 


30 


17-8 


19-1 


20'5 


22'2 


24-2 


26-6 


29-5 


33'2 


37'9 


44-2 


53' 


66-2 


88-3 


132 


265 


31 


18-0 


I9-3 


20-7 


22'4 


24-5 


26-9 


29-8 


33'5 


38-3 


44 -6 


53*5 


66-9 


89-2 


134 


267 


32 


18-2 


i9'5 


2I'O 


22'7 


24-7 


27-2 


30-2 


33'9 


38'7 


45'i 


54' 1 


67-6 


90-1 


135 


270 


33 


18-4 


19-7 


21'2 


22'9 


25-0 


27'5 


3'5 


34'3 


39' i 


45-6 


54'7 


68-4 


91-1 


137 


273 


34 


18-6 


19-9 


21'4 


23'2 


25'3 


27-8 


30-8 


34'7 


39-6 


46-2 


55'4 


69*2 


92-2 


138 


276 


35 


18-9 


2O'2 


21'7 


23-5 


25-6 


28-1 


31-2 


35'i 


40-1 


46-7 


56-0 


70-0 


93-3 


140 


280 


36 


19-1 


20'4 


22*0 


23-8 


25*9 


28-5 


31-6 


35'5 


40*6 


47*3 


56-7 


70-9 


94'5 


142 


283 


37 


19-4 


20'7 


22'3 


24-1 


26-2 


28-8 


32-0 


36*0 


41-1 


47'9 


57*5 


71-8 


95'7 


144 


287 


38 


19-6 


21'0 


22'6 


24-4 


26-6 


29-2 


32-4 


36-5 


41-7 


48-6 


58-2 


72-8 


97-0 


145 


291 


39 


19-9 


21'3 


22'9 


2 4 -8 


27-0 


29*6 


32-9 


37' 


42-2 


49-2 


59'i 


73-8 


98-3 


147 


295 


40 


20'2 


21-6 


23-2 


2 5 -I 


27-4 


30-1 


33'4 


37'5 


42-8 


50-0 


59'9 


74'9 


99'8 


150 


299 


4 1 


20-5 


21'9 


2 3 -6 


25*5 


27-8 


30-5 


33'9 


38-1 


43*5 


50*7 


60-8 


76-0 


IOI 


152 


304 


42 


20-8 


22'2 


23-9 


25-9 


28-2 


31-0 


34*4 


38-7 


44'2 


5i-5 


61-8 


77*2 


103 


154 


308 


43 


2I'I 


22-6 


24-3 


26-3 


28-7 


3i-5 


35 'P 


39'3 


44'9 


52-3 


62-8 


78-4 


105 


157 


313 


44 


21-5 


23-0 


24-7 


26-7 


29-1 


32-0 


35'5 


40-0 


45-6 


53'2 


63-8 


79'7 


1 06 


159 


319 


45 


21-9 


23M 


25-1 


27-2 


29-6 


32-6 


36-2 


40-6 


46-4 


54' i 


64-9 


81-1 


108 


162 


324 


46 


22*2 


23-8 


25-6 


2 7 - 7 


30-2 


33-2 


36-8 


41-4 


47*2 


55'i 


66-1 


82-5 


no 


165 


330 


47 


22'7 


2 4 '2 


26-1 


28-2 


30-7 


33-8 


37*5 


42-1 


48-1 


56-1 


67-3 


84-1 


112 


168 


336 


48 


23-I 


24-7 


26-6 


28-8 


3i'3 


34'4 


38-2 


43'0 


49-1 


57*2 


68-6 


85-7 


114 


171 


343 


49 


2 3 -6 


25-2 


27-1 


29'3 


32-0 


35'i 


39-0 


43-8 


50*0 


58-3 


70-0 


87-4 


!l6 


I7 I 


349 


50 


24-0 


257 


27'7 


29-9 


32-6 


35-8 


39'8 


44'7 


51-1 


59'5 


71-4 


89-2 


119 


178 


357 


5i 


2 4 -6 


26-3 


28-3 


30-6 


33'3 


36-6 


40-6 


45'7 


52-2 


60-8 


72-9 


91-1 


121 


182 


364 


53 


25-I 


26-9 


28-9 


31-2 


34'i 


37'4 


4i'5 


46-7 


53'3 


62-2 


74'5 


93'i 


124 


1 86 


372 


53 


25'7 


27'5 


29'5 


32-0 


34-8 


38'3 


42'5 


47-8 


54'5 


63-6 


76-3 


95'3 


127 


190 


381 


54 


26-3 


28-1 


30-3 


32-7 


35'7 


39-2 


43-5 


48-9 


55-8 


6 5 "i 


78-1 


97-6 


. I 3 


195 


390 


55 


26-9 


28-8 


31-0 


33'5 


36-5 


40-2 


44 -6 


50-1 


57'2 


66-7 


80-0 


lOO'O 


133 


200 


400 


56 


27-6 


29-6 


31*8 


34'4 


37*5 


41-2 


45'7 


5i'4 


58-7 


68-4 


82-1 


IO2'5 


137 


205 


410 


57 


28-4 


3'4 


32-6 


35'3 


38-5 


42-3 


46-9 


52-8 


60-3 


70-3 


84-3 


105-3 


140 


210 


421 


58 


29-2 


31-2 


33'6 


36-3 


39-6 


43'5 


48-3 


54'2 


61-9 


72-2 


86-6 


108-2 


144 


216 


432 


59 


30-0 


32-1 


34'5 


37'4 


40-7 


44*7 


49-6 


55-8 


63'7 


74*3 


89- ! 


III'; 


148 


223 


445 


60 


30-9 


33'i 


35-6 


38-5 


41-9 


46-1 


5i-i 


57'5 


65-6 


76-5 


91-8 


114-7 


153 


229 


458 



To convert time into longitude divide by 4. Thus 35-6 s. -r- 4 = 8-9' long. 



6 Azimuth 



82 
Table D. 

SHOWING THE ERROR PRODUCED IN THE TIME OR LONGITUDE BY AN ERROR OF i' IN THE 

ALTITUDE. 



Azamuths. I 


LATITUDES. 


61 


62 


63 


64 


65 


66 


67 


68 


69 


70 


71 


72 


73 


74 


75 




S. 


s 


S. 


S. 


S. 


S. 


S. 


S. 


S. 


S. 


S. 


s 


s 


S S 


?i 


945 


976 


1010 


1046 


1085 


1127 


H73 


I22 4 


1279 


1340 


1408 


1483 


1568 


1663 1771 


i 


473 


488 


505 


523 


542 


563 


587 


612 


6 4 


6 7 


704 


742 


784 


832 886 


ii 


3i5 


325 


337 


349 


362 


376 


391 


408 


426 


447 


469 


495 


523 


554 i 590 


2 


236 


244 


252 


262 


2 7 I 


282 


293 


306 


320 


335 


352 


37i 


392 


416 


443 


2* 


189 


195 


202 


209 


217 


225 


235 


245 


2 5 6 


268 


282 


297 


314 


333 


354 


3 


158 


163 


168 


J 74 


181 


188 


I 9 6 


204 


213 


223 


235 


247 


261 


277 


295 


32 


135 


140 


144 


150 


155 


161 


168 


J 75 


183 


192 


2O I 


212 


224 


237 


253 


4 


118 


122 


126 


131 


136 


141 


147 


153 


160 


168 


I 7 6 


1 86 


196 


208 


222 


^ 


105 


109 


112 


116 


121 


125 


130 


136 


142 


149 


J 57 


165 


174 


185 


197 


5 


947 


97'8 


101 


105 


109 


ii3 


117 


123 


128 


134 


141 


149 


157 


167 


177 


5 


86-1 


88-9 


9I-9 


95'2 


98-8 


103 


107 


in 


116 


122 


128 


135 


143 


151 


161 


6 


79-1 


81-5 


84-3 


87-3 


90-5 


94-1 


97-9 


102 


107 


112 


118 


124 


J 3i 


139 


I 4 8 


?i 


72-9 


75'3 


77-8 


80-6 


83-6 


86-9 


90-4 


94'3 


98-6 


103 


109 


114 


121 


128 


J 37 


7 


677 


69-9 


72-3 


74'9 


777 


807 


84-0 


87-6 


91-6 


96-0 


IOI 


1 06 


112 


119 


127 


ft 


63-2 


65-3 


67-5 


69-9 


72-5 


75'3 


78-4 


8r8 


85-5 


89-6 


94-1 


99-2 


IO5 


in 


118 


8 


59'3 


61-2 


63-3 


65-6 


68-0 


707 


73-6 


767 


80-2 


8 4 -0 


88-3 


93-0 


98-3 


104 


in 


8& 


55-8 


57-6 


59'6 


617 


64-0 


66-5 


69-3 


72-2 


75'5 


79'I 


83-1 


87-6 


92-6 


98-2 


105 


9 


527 


54'5 


56-3 


58-3 


60-5 


62'9 


65H 


68-3 


71-4 


74-8 


78-5 


827 


87-5 


92-8 


98-8 


9i 


50-0 


51-6 


53'4 


55*3 


57'3 


59'6 


62-0 


647 


67-6 


70-9 


74'4 


78-4 


82-9 


87-9 


93-6 


10 


47'5 


49*i 


50'7 


52-6 


54*5 


56-6 


59'o 


61-5 


64-3 


67-4 


70-8 


74*5 


78-8 


83-6 


89-0 


lOfc 


45'3 


46-8 


48-3 


50-1 


5i'9 


54' 


56-2 


58-6 


61-2 


64-2 


67-4 


71-0 


75'i 


79-6 


84-8 


ii 


43'2 


447 


46-2 


47'8 


49-6 


5V5 


537 


56-0 


58-5 


61-3 


64-4 


67-8 


717 


76-1 


81-0 


"4 


41-4 


427 


44-2 


45'8 


47*5 


49'3 


51*3 


53'6 


56-0 


587 


61-6 


64-9 


68-6 


72-8 


77'5 


12 


39' 7 


41-0 


42-4 


43'9 


45'5 


47'3 


49-2 


5i-4 


537 


56-3 


59'i 


62-3 


65-8 


69-8 


74'3 


ia* 


38-1 


39'4 


407 


42-2 


437 


45'4 


47'3 


49*3 


51-6 


54 - o 


56-8 


59'8 


63-2 


67*0 


71-4 


13 


367 


37'9 


39-2 


40-6 


42-1 


43'7 


45'5 


47*5 


49-6 


52-0 


54-6 


57'5 


60-8 


64-5 


687 


I3i 


35'3 


36-5 


37'7 


39'i 


4'5 


42-1 


43'9 


457 


47-8 


50-1 


52-6 


55*4 


58-6 


62-2 


66-2 


H 


34' i 


35*2 


36-4 


377 


39'i 


407 


42-3 


44-1 


46- 1 


48-3 


50-8 


53-5 


56-6 


60-0 


63-9 


H* 


33'0 


34'o 


35-2 


36-4 


37'8 


39'3 


40-9 


42-6 


44-6 


467 


49-1 


5i7 


54*6 


58*0 


617 


15 


3 J '9 


32*9 


34*o 


35-3 


36-6 


38-0 ; 39-6 


4i-3 


43-i 


45'2 


47'5 


50-0 


52-9 


56-1 


597 


x$* 


30-9 


3i-9 


33'0 


34*i 


35'4 


36-8 


383 


40-0 


41-8 


43-8 


46-0 


48-4 


51-2 


54'3 


57'8 


16 


29-9 


30-9 


32-0 


33'i 


34'3 


357 


37'i 


387 


40' 5 


42-4 


44-6 


47-0 


49-6 


52-6 


56-1 


i6i 


29' i 


30-0 


31-0 


32-1 


33-3 


34'6 


36^0 


37'6 


39'3 


41-2 


43'3 


45-6 


48-2 


5i'i 


54'4 


J 7 


28-2 


29-1 


30-1 


31-2 


32-4 


33'6 


35'o 


36-5 


38-2 


40-0 


42-0 


44'3 


46-8 


49-6 


52-9 


i7* 


27-4 


28-3 


29*3 


30'3 


3i'5 


32*7 


34'o 


35'5 


37-i 


38-9 


40-9 


43-o 


45'5 


48-3 


51'4 


18 


267 


27-6 


28-5 


29' 5 


30*6 


31-8 


33'i 


34-6 


36-1 


37-8 


39*8 


41-9 


44'3 


47-0 


50-0 


18* 


26'O 


26-9 


27-8 


28-8 


29-8 


31-0 


32*3 


337 


35'2 


36-9 


387 


40-8 


43'i 


457 


487 


iQ 


25-3 


26-2 


27-1 


28-0 


29-1 


30-2 


3i'4 


32-8 


34'3 


35'9 


377 


39'8 


42'O 


44-6 


47'5 


19* 


247 


25'5 


26-4 


27-3 


28-4 


29-5 


307 


32-0 


33H 


35*0 


36-8 


38-8 


41-0 


43'5 


46-3 


20 


24-1 


24-9 


25-8 


267 


277 


28-8 


29'9 


3i'2 


32-6 


34'2 


35'9 


37-8 


40-0 


42-4 


45'2 


20^ 


23-6 


24-3 


25-2 


26-1 


27-0 


28-1 


29-2 


30-5 


3i*9 


33'4 


35'i 


37' 


39'i 


41-4 


44-1 


21 


23-0 


23-8 


24-6 


25-5 


26-4 


27*4 


28-6 


29-8 


31-1 


32-6 


34*3 


36-i 


38-2 


40-5 


43'i 


2li 


22'5 


23-2 


24*0 


24-9 


25-8 


26-8 


27-9 


29-1 


30-5 


3i-9 


33-5 


35'3 


37'3 


39-6 


42-2 


22 


22'O 


227 


23*5 


24-4 


25-3 


26-3 


27-3 


28-5 


29-8 


31-2 


32-8 


34'6 


36-5 


387 


4*'3 


22^ 


21'6 


22-3 


23-0 


23-8 


247 


257 


26-8 


27-9 


29-2 


30-6 


32-1 


33-8 


35-8 


37*9 


40-4 


23 


21*1 


21-8 


22-5 


23-3 


24-2 


25*2 


26'2 


27'3 


28-6 


29-9 


3i'4 


33'i 


35-o 


37'i 


39-6 


23* 


207 


21-4 


22'J 


22-9 


237 


247 


257 


26-8 


28-0 


293 


30-8 


32'5 


34'3 


36-4 


38-8 


24 


20-3 


20-9 


217 


22- 4 


23'3 


24-2 


25-2 


26-3 


27-4 


28-8 


30-2 


31-8 


33-6 


357 


38-0 


24l 


19-9 


20-5 


21'2 


22'O 


22-8 


237 


247 


257 


26-9 


28-2 


29*6 


31-2 


33'o 


35'0 


37'3 


25 


I9-5 


20*2 


20-8 


21'6 


22'4 


23-3 


24-2 


25-3 


26-4 


277 


29-1 


30-6 32-4 


34'3 


36-6 


25^ 


I9-2 


19-8 


20-5 


21'2 


22'0 


22-8 


2 3 -8 


24-8 


25'9 


27-2 


28-5 


30-1 31*8 


337 


35'9 


26 


18-8 


19-4 


20' I 


20-8 


21-6 


22- 4 


23-4 


24-4 


25-5 


267 


28-0 


29-5 31-2 


33'i 


35'3 


26* 


18-5 


19-1 


197 


20- 4 


21*2 


22'0 


22'9 


23-9 


25-0 


26-2 


27'5 


29-0 307 


32-5 


34'6 


27 


18-2 


18-8 


I9- 4 


20-1 


20-8 


217 


22'5 


23'5 


24-6 


25-8 


27-1 


28-5 30-1 


32-0 


34' 


27 


17-9 


18-5 


I9-I 


19-8 


20-5 


21-3 


22*2 


23-1 


24-2 


25-3 


26-6 


28-0 29-6 


3*'4 


33'5 


28 


17-6 


18-1 


18-8 


19-4 


2O'2 


20'9 


21-8 


227 


23-8 


24-9 


26-2 


27*6 29'! 


30-9 


32-9 


28 


i7'3 


17-9 


18-5 


I9-I 


19-8 


2O'6 


21'5 


22-4 


23*4 


24-5 


257 


27-1 287 


30-4 


32-4 


29 


17-0 


17-6 


18-2 


18-8 


I9-5 


20-3 


2I'I 


22'0 


23-0 


24-1 


25'3 


267 28'2 


29-9 


3i'9 


29* 


16-8 


*7'3 


17-9 


18-5 


I9-2 


20'0 


20-8 


217 


227 


23-8 


25-0 


26-3 27-8 


29'5 


3i-4 


30 


16-5 


17-0 


17-6 18-2 


l8'9 


197 


20'5 


21'4 


22-3 


23H 


24-6 


25-9 27-4 


29-0 


30-9 



To convert time into longitude divide by 4. Thus 29-25. -r- by 4 = 7-3' longitude. 






83 

Table D. 

SHOWING THE ERROR PRODUCED IN THE TIME OR LONGITUDE BY AN ERROR OF i' IN THE 

ALTITUDE. 



Jr. 


LATITUDES. 


76 


77 


78 


79 


80 


804" 


81 


81* 


82 82J= 


83 


83^ 


1 
84 8*i 

i 


85 




S. 


s. 


S. 


S. 


S 


s. 


S. 


s. 


s 


s 


s 


s 


g 


s 


g 


o$ 


1895 


2038 


2205 


2402 


2640 


2777 


2930 


3101 


3294 


3512 


3761 


4049 


4385 


4782 


5259 


I 


947 


1019 


IIO2 


1201 


1320 


1389 


I 4 66 


1551 


1647 


1756 


1881 


2025 


2193 


2391 


2630 


J $ 


632 


679 


735 


80 1 


880 


926 


977 


1034 


1098 


1171 


1254 


1350 


1462 


1594 


1753 


j 


474 


510 


551 


60 1 


660 


694 


733 


775 


824 


878 


940 


1012 


1096 


1193 




2$ 


379 


408 


441 


4 8l 


528 


556 


586 


620 


659 


703 


752 


810 


877 


957 


1052 


3 


316 


34 


368 


4 OI 


440 


463 


489 


517 


549 


586 


627 


675 


731 


797 


877 


3$ 


271 


291 


315 


343 


377 


397 1 419 


443 


47 1 


502 


538 


579 


627 


684 


752 


4 


2 37 


255 


276 


301 


330 


347 | 367 


388 


412 


439 


47 1 


507 


549 


598 


658 




211 


227 


245 


267 


294 


309 


326 


345 


366 




418 


450 


488 


532 


585 


5 


190 


204 


221 


241 


264 


278 


293 


310 


330 


352 


377 


405 


439 


479 


527 


5$ 


^73 


1 86 


2O I 


219 


240 


253 


267 


282 300 


320 


342 


369 


399 


435 


479 


6 


158 


170 


184 ; 201 


220 


232 


245 


259 275 


293 


3M 


338 


366 


399 


439 


6$ 


I 4 6 


157 


170 185 


203 


214 


226 


239 254 


271 


290 


312 


338 


369 


405 


7 


I 3 6 


146 


158: 172 


189 


199 


210 


222 236 


251 


269 


290 


3M 


343 


377 




127 


136 


147 j 161 


176 


1 86 


I 9 6 


207 220 


235 


251 


271 


293 


320 


352 


8 


119 


128 


138 


151 


1 66 


174 


I8 4 


194 


207 


220 


236 


254 


275 


300 


330 


8A 


112 


120 


130 


142 


156 


164 


173 


I8 3 


194 


207 


222 


239 


259 


282 


311 


9 


1 06 


114 


123 


134 


147 


155 




173 


184 


196 


2IO 


226 


245 


267 


293 




100 


108 


117 127 


140 


147 


155 




174 


1 86 


199 


214 


232 


253 


278 


10 


95'2 


102 


III 121 


133 


140 


H7 


156 


1 66 


176 


189 


203 


220 


240 


264 


ro| 


907 


97'6 


loG 115 


126 


133 


I 4 


! 4 8 


158 


168 


1 80 


194 


2IO 


229 


252 


ii 


867 


93-2 


101 no 


121 


127 




I 4 2 




161 


172 


185 


201 


219 


241 


n$ 


82-9 


89-2 


96-5 105 


1x6 


122 


128 


I 3 6 


144 


154 


165 


177 


IQ2 


209 


230 


12 


79'5 


85-5 


92-5 i 01 


in 


117 


123 


130 


138 


147 


158 


170 


I8 4 


2OI 


221 


12$ 


76-4 


82-2 


88' 9 96-9 


106 


112 


118 


125 


133 


142 


152 


163 


177 


193 


212 


I3 


73'5 


79-0 


85-5 93'2 


102 


1 08 


114 


I 2O 


128 


136 


I 4 6 


157 


170 


186 


20 4 


jol 


70-8 


7 6-2 


82-4 89-8 


987 


104 


no 


1x6 


123 


131 


141 


151 


I6 4 


179 


197 


T 4 


68-3 


73'5 


79-5 867 


95'2 


100 ;;o6 


112 


119 


127 


I 3 6 


146 


158 


173 


190 


M$ 


66-0 


71-0 


76-8 


837 


92-0 


g6'S 102 


108 


"5 


122 


I 3 I MI 


153 


167 


I 83 


15 


63-9 


687 


74'3 


81-0 


89-0 


93'6 98-8 


105 


in 


118 


127 137 


I 4 8 


161 


177 


I5 i 


61*9 


66-5 


72-0 


78-4 


86-2 


907 957 


101 


108 


"5 


I2 3 132 


143 


156 


172 


16 


60*0 


64-5 


60-8 


76-0 


83-6 


87'9 92-8 


98-2 


104 


in 


119 128 


139 


151 


167 




58-2 


62-6 


677 73-8 


8ri 


85-3 90-0 


95-3 


101 


1 08 


116 


124 


135 


147 


161 


17 


56-6 


60-8 


65-8 


717 


78-8 


82-9 


87-5 


92*6 


98-3 


105 


112 


121 


I 3 I 


M3 


157 


i7$ 


55'o 


59' i 


64^0 


697 


76-6 


80-6 


85-0 


90-0 


95*6 


102 


109 n8 


127 


139 


153 


18 


53'5 


57'5 


62-3 


67-8 


74'5 


78-4 827 


87-6 


93-0 


99-2 


I 06 j 114 


124 


135 


149 


1 8$ 


52-1 


56-0 


60-6 


66-1 


72-6 


76-4 


80-6 


85-3 


90-6 


96-6 


103 


III 


121 


132 


145 


19 


50-8 


54'6 


59' i 


64-4 


70-8 


74'4 


78-5 


83-1 


88-3 


94'I 


101 


109 


118 


128 


141 


19$ 


49'5 


53'3 




62-8 


69-0 


72-6 


76-6 


8ri 


86-1 


91-8 


98-3 


1 06 


115 


125 


137 


20 




52-0 


56-3 


61-3 


67-4 


70-9 


74-8 


79-1 


84-0 


89-6 


96-0 


103 


112 


122 


*34 


20* 


47' 2 


50-8 


54'9 


59'9 


65-8 


69-2 


73' 


77'3 


82-1 


87-5 


937 


101 


109 


119 


131 


21 


46-1 


49-6 


537 


58-5 


6 4' 3 


67-6 




75'5 


80-2 


85-5 


91-6 


98-6 


107 


116 


128 


21$ 


45' 1 




52-5 




62-9 


66-1 


69-8 


73'8 


78-4 


83-6 


89-6 


96-4 


I0 4 


114 


125 


22 


44' I 


47"5 




56-0 


61-5 


647 


68-3 


72-2 


767 


81-8 


87-6 


94'3 


IO2 


XII 


123 


22^ 






50-3 


54'8 


60-2 


6 3'3 


66-8 


707 


75'i 


80- 1 


85-8 


92-3 


IOO 


109 


120 


23 
23$ 


42'3 
4 T '5 


45'5 
44-6 


49'2 
48-2 


537 
52-6 


59'o 
57'8 


62'O 

60-8 


65-4 
64*1 


69-3 
67-9 


73-6 
72-1 


78-4 
76-9 


84-0 
82-3 


90-4 

88-6 


97-9 

96-0 


107 
105 


117 


24 
24$ 

25 


407 
39'9 


437 
42'9 
42-1 


47'3 
46-4 
45'5 


5^5 
50-5 
49-6 


56-6 
55'5 
54'5 


596 

58-4 

57'3 


62-9 

617 
60-5 


66-5 
65-3 
64-0 


707 
69-3 
68-0 


75'3 
73'9 


807 
79-1 

777 


86-9 
85-2 
83-6 


94-1 
92-3 
90-5 


103 

101 

98-8 


III 
109 


2 5$ 
26 


38-4 
377 


4 I- 3 


447 
43'9 


487 
47-8 


53'5 


56-3 
55'3 


59'4 
58-3 


62 9 

617 


66-8 
65-6 


71-2 
69-9 


76-2 
74'9 


82-1 
80-6 


88-9 

87-3 


96-9 ' 107 
95-2 105 


26$ 


37 'i 


39'9 




47-0 


51-6 


54'3 


57'3 


60-6 


64-4 


687 


73;6 


79-2 


85-8 


93'5 103 


27 
27$ 


36-4 
35-8 


39'2 


42-4 
417 


46-2 
45'4 


507 
49'9 


53'4 
52-5 


56-3 
55'4 


59-6 
58-6 


62-2 


67-5 
66-4 


71-1 


77-8 
7 6> 5 


84-3 
82-9 


gi'9 ! 101 

90-4 ! 99-4 


28 




37'9 


41-0 


447 


49-1 


5 r6 


54'5 


57-6 


61-2 


65-3 


69-9 


75'3 


8i'5 


88-9 97-8 


28$ 


347 


37'3 


4' 3 


43'9 




50*8 


53-6 


567 


60-2 


64-2 


68-8 


74' 1 


80-2 


87-5 96-2 


29" 
29$ 


34' I 
33'6 


367 
36-1 


397 43-2 
39-1 ! 42-6 


47'5 
46-8 


49'2 


527 
5^9 


55-8 


59' 3 

58-4 


63-2 
62-2 


677 
667 


72-9 

71-8 


78-9 
777 


86-1 
84-8 


947 


J & 

30 




35'6 38-5 


41-9 46-1 


48'5 




54' 1 


57'5 


61-3 


65-6 


707 


7 6 '5 j 3'5 


91-8 



















To convert time into longitude divide by 4. Thus 5 o'8s. 4- by 4 = 127' longitude. 



84 
Table D. 

SHOWING THE ERROR PRODUCED ix TUB TIMS OR LOKQITUDK ay AN ERROR OF i' 

ALTITUDE. 



IX TMK 



Azimuths. I 


LATITUDES. 


61 


82 


63 


64 


65 


66 


67 


68 


69 


69i 


70 


70i 


71 


71i 


72 














1 












o 


S. 


S. 


S. 


s. 


s. 


S. 


S. 


S. S. 


S. 


s. 


S. 


S. 


s. 


s. 


30 


16-5 


I7-0 


17-6 


18-2 


i8'9 


197 


20-5 


21-4 


22'3 


22'8 


23*4 


24-0 


2 4 -6 


25-2 


25'9 


3 1 


16-0 


16-5 


17-1 


17-7 


18-4 


I9-I 


19-9 


207 


21'7 


22'2 


227 


23-3 


23-9 


24'5 


25-1 


32 


15-6 


16-1 


16-6 


17-2 


17-9 


18-6 


19-3 


20'I 


2I'I 


21'6 


22'I 


22'6 


23'2 


23-8 


24-4 


33 


15-1 


15-6 


16-2 


16-8 


17-4 


18-1 


18-8 


ig'6 


20'5 


21'0 


21-5 


22'O 


22'6 


23-1 


23-8 


34 


14-8 


i5'2 


15-8 


16-3 


i6'9 


17-6 


18-3 


19-1 


2O'O 


2O'4 


20-9 


21-4 


22'0 


22'5 


23-1 


35 


14-4 


14-9 


15-4 


I5-9 


16-5 


17-1 


17-8 


18-6 


19*5 


I9'9 


20-4 


20-9 


21' 4 


22'O 


22'6 


36 


14-0 


M'5 


15-0 


i5'5 


16-1 


167 


17-4 


18-2 


I9'0 


I9'4 


19-9 


20-4 


20-9 


21' 4 


22'0 


37 


137 


14-2 


14-6 


15-2 


157 


16-3 


17-0 


177 


18-5 


I9'O 


19-4 


19-9 


20'4 


20-9 


21-5 


33 


I3M 


13-8 


14-3 


14-8 


i5'4 


16*0 


16-6 


i7'3 


18-1 


18-6 


19-0 


19-5 


2O'O 


20-5 


21'0 


39 


13-1 


I3-5 


14-0 


M'5 


15-0 


15-6 


16-3 


17-0 


177 


18-1 


18-6 


19-0 


I9'5 


2O'O 


20'6 


40 


12-8 


I3-3 


137 


14-2 


147 


I5'3 


I5'9 


16-6 


17-4 


17-8 


18-2 


iS-6 


I9'I 


19-6 


20'I 


4 1 


12-6 


13-0 


13-4 


i3'9 


14-4 


15-0 


15-6 


16-3 


17-0 


17-4 


17-8 


18-3 


187 


19-2 


197 


42 


12-3 


127 


13-2 


i3'6 


14-1 


147 


I5-3 


16-0 


167 


17-1 


i7'5 


17-9 


18-4 


18-8 


19-3 


43 


I2'I 


12-5 


12-9 


I3H 


I3'9 


14-4 


15-0 


157 


16-4 


167 


17-1 


17-6 


18-0 


18-5 


19-0 


44 


11-9 


12-3 


12-7 


i3'i 


13-6 


14-2 


147 


J 5'4 


16-1 


16-4 


16-8 


i?'3 


177 


18-1 


iS-6 


45 


11-7 


I2'O 


12-5 


12-9 


I3'4 


I3'9 


i4'5 


I5'i 


15-8 


!6'2 


16-5 


16-9 


17-4 


17-8 


18-3 


46 


*5 


ii-8 


I2'2 


12-7 


13-2 


137 


14-2 


14-8 


15*5 


15*9 


16-3 


167 


17-1 


17*5 


18-0 


47 


ii*3 


ii-6 


I2'O 


12-5 


12-9 


I3H 


14-0 


14-6 


I5'3 


15-6 


16-0 


16-4 


16-8 


17-2 


177 


48 


ii'i 


"*5 


11-9 


12-3 


127 


13-2 


13-8 


14-4 


15-0 


15*4 


157 


i6'i 


16-5 


17-0 


17-4 


49 


10-9 


11-3 


11-7 


I2'I 


12-5 


13-0 


13-6 


14-1 


14-8 


I5' 1 


i5'5 


15*9 


16-3 


167 


17-2 


50 


10-8 


in 


"'5 


11-9 


12-4 


12-8 


I3H 


I3-9 


14-6 


14-9 


15-3 


15-6 


i6'o 


16-5 


i6'9 


51 


iO'6 


II'O 


ii'3 


117 


I2'2 


127 


13-2 


137 


14-4 


147 


15-0 


I5'4 


15-8 


16-2 


167 


52 


10-5 


10-8 


11*2 


ii-6 


I2'0 


12-5 


13-0 


13-6 


I 4 '2 


14-5 


14-8 


15-2 


i5'6 


i6'o 


16-4 


53 


10-3 


10-7 


II'O 


11-4 


II'9 


12-3 


I2'8 


I3'4 


I 4 '0 


H'3 


14-6 


15-0 


I5H 


15-8 


16-2 


54 


I0'2 


10-5 


io'9 


n'3 


117 


I2'2 


127 


13-2 


13-8 


14-1 


H'5 


14-8 


15-2 


I5'6 


16-0 


55 


lO'I 


10-4 


io-8 


ii'i 


n-5 


I2'O 


12-5 


13-0 


13-6 


I3-9 


I4'3 


14-6 


15-0 


I5H 


15-8 


56 


9'95 


10-3 


10-6 


II'O 


11-4 


ii-9 


12-3 


12-9 


I3'5 


13*8 


14-1 


I4'5 


14-8 


15-2 


i5'6 


57 


9-84 


IO'2 


10-5 


io'9 


ii'3 


117 


I2'2 


127 


IS'S 


13-6 


I3-9 


H'3 


14-6 


15-0 


J 5'4 


58 


973 


IO'O 


io'4 


10-8 


II'2 


ii-6 


I2'I 


I2'6 


I3'2 


13*5 


13-8 


14-1 


i4'5 


14-9 


15-3 


59 


9-63 


9'94 


10-3 


io'6 


II'O 


ii'5 


II'9 


12-5 


I3'0 


13-3 


13-6 


14-0 


i4'3 


147 


i5'i 


60 


9'53 


9-84 


10-2 


10-5 


10-9 


ir-4 


n-8 


12-3 


12-9 


13-2 


i3'5 


i 3 '8 


14-2 


14-6 


14-9 


61 


9'43 


974 


lO'I 


io'4 


10-8 


n'2 


117 


I2'2 


I2'8 


13-1 


i3'4 


137 


14-0 


14-4 


14-8 


62 


9*34 


9'65 


lO'O 


10-3 


107 


ii'i 


ii-6 


I2'I 


I2'6 


12-9 


13-2 


13-6 


13*9 


i4'3 


147 


63 


9'26 


9'56 


9^9 


IO'2 


iO'6 


II'O 


ii'5 


I2'0 


12-5 


I2'8 


13-1 


i3'4 


13-8 


14-1 


I4-5 


64 


9-18 


9-48 


9'80 


IO'2 


10-5 


10-9 


1 1-4 


ii'9 


12-4 


127 


13-0 


*3'3 


137 


14-0 


14-4 


65 


9'io 


9-40 


972 


lO'I 


io'4 


io*9 


ii'3 


n-8 


12-3 


I2'6 


12-9 


13-2 


13-6 


i3'9 


14-3 


66 


9-03 


9'33 


9-64 


9-99 


10-4 


10-8 


II'2 


117 


I2'2 


12-5 


I2'8 


13-1 


I3'4 


13-8 


14-2 


67 


8-96 


9'26 


9'57 


9-9I 


10-3 


107 


II'I 


n-6 


I2'I 


12-4 


127 


13*0 


13*3 


137 


14-1 


68 


8-90 


9-19 


9-50 


9-84 


IO'2 


10-6 


II'O 


ii'5 


I2'O 


12-3 


I2'6 


12-9 


I3-3 


13-6 


14-0 


69 


8-8 4 


9-13 


9-44 


977 


lO'I 


10-5 


II'O 


11-4 


I2'0 


I2'2 


12-5 


12-8 


13-2 


13*5 


I3-9 


70 


8-78 


9-07 


9-38 


9-71 


io-i 


10-5 


io'9 


ii' 4 


11-9 


I2'2 


12-4 


I2'8 


13-1 


I3H 


13-8 


7i 


8-73 


9'oi 


9-32 


9-65 


lO'O 


10-4 


10-8 


11-3 


ii-8 


I2'I 


12-4 


127 


13-0 


I3-3 


137 


72 


8-68 


8-96 


9-26 


9'59 


9'95 


10-3 


10-8 


II'2 


117 


I2'0 


12-3 


I2'6 


I2'9 


I3-3 


13-6 


73 


8-63 


8-91 


9-21 


9'54 


9-90 


10-3 


107 


II'2 


117 


11-9 


I2'2 


12-5 


I2'8 


13-2 


I3-5 


74 


8-58 


8-86 


9-17 


9'49 


9^5 


IO'2 


io'6 


II'I 


ii-6 


ii'9 


I2'2 


12-5 


I2'8 


13-1 


I3'5 


75 


8-54 


8-82 


9-12 


9'45 


9-80 


IO'2 


io'6 


II'I 


ii-6 


ii-8 


I2'I 


12-4 


127 


13-1 


13*4 


76 


8-50 


8-78 


9-08 


9-40 


975 


IO'I 


I0'6 


II'O 


ii'5 


ii-8 


I2'I 


12-3 


127 


13-0 


13*3 


77 


8-47 


8-74 


9-04 


9-36 


9-71 


lO'I 


10-5 


II'O 


n-5 


117 


I2'O 


12-3 


I2'6 


12-9 


i3'3 


78 


8-44 


8-71 


9-01 


9'33 


9-68 


lO'I 


10-5 


io'9 


11-4 


117 


I2'0 


12-3 


I2'6 


12-9 


13-2 


79 


8-41 


8-68 


8-98 


9-30 


9-64 


lO'O 


10-4 


io'9 


11-4 


ix-6 


II'9 


I2'2 


12-5 


I2'8 


13-2 


80 


8-38 


8-65 


8'95 


9-27 


9-61 


9-99 


io'4 


io-8 


ii'3 


ii-6 


n-9 


I2'2 


12-5 


I2'8 


13** 


3 1 


8-35 


8-63 


8-92 


9-24 


9-58 


9-96 


10-4 


10-8 


n'3 


n-6 


11-8 


I2'I 


12-4 


I2'8 


13-1 


Sz 


8-33 


8-60 


8-90 


9-21 


9-56 


9'93 


10-3 


10-8 


ii'3 


n*5 


11-8 


I2'I 


12-4 


127 


13-1 


83 


8-31 


8-58 


8-88 


9-19 


9'54 


9-91 


10-3 


io-8 


11*2 


ii'5 


11-8 


I2'I 


12-4 


127 


13-0 


84 


8-30 


8-57 


8-87 


9-17 


9-52 


9-89 


10-3 


107 


II'2 


n'5 


u-8 


I2'O 


12-4 


127 


13-0 


8 5 


8-28 


8-55 


8-84 


9-16 


9-50 


9-87 


20-3 


107 


II'2 


n*5 


117 


I2'O 


12-3 


127 


13-0 


86 


8-27 


8'54 


8-83 


9'i5 


9'49 


9-86 


10-3 


107 


II'2 


11-4 


117 


I2'0 


12-3 


I2'6 


13-0 


8? 


8-26 


8-53 


8-82 


9-14 


9-48 


9-85 


10-3 


107 


II'2 


11-4 


117 


I2'0 


12-3 


I2'6 


13-0 


88 


8-26 


8-53 


8-82 


9'i3 


9'47 


9-8 4 


I0'2 


107 


11*2 


11-4 


117 


I2'0 


12-3 


I2'6 


13-0 


89 


8-25 


8-52 


8-81 


9-13 


9*47 


9-84 


I0'2 


107 


II'2 


11-4 


117 


I2'O 


12-3 


I2'6 


12-9 


90 


8-25 


8-52 


8-81 


9-12 


9H6 


9-83 


IO'2 


107 


II'S 


11-4 


117 


I2'O 


12-3 


I2'6 


12-9 



To convert time into longitude divide by 4. Thus ns. * 4 = 3' long. 



85 



Table D. 

SHOWING THE ERROR PRODUCED IN THE TIME OR LONGITUDE BY AN ERROR OF i ( 

ALTITUDE. 



IN THE 



Azimuths. 1 


LATITUDES. 


73 


74 


75 


76 


77 


78 


' 79 


80 


81 


82 


83 


83J 


84 


84* 


85 












s. 


S. 


S. 




S. 














30 


27-4 


29-0 


30-9 




35-6 


38-5 


41-9 


4 6-I 




57'5 


65-6 


707 


76-5 




91-8 


31 


26-6 


28-2 


30-0 


32-1 


34*5 


37'4 


407 


447 


49-6 


55-8 


637 


68-6 


74'3 


Si-o 


89-1 


32 


25-8 


27*4 


29-2 


3 l-2 


33-6 


36-3 


39-6 


43*5 


48'3 


54' 2 


61-9 


667 


72-2 


78-8 


86-6 


33 


2 5 -l 


26-6 


28-4 


30-4 


32-6 


35'3 


38*5 


42-3 


46-9 


52-8 


60-3 


64-9 


70-3 


76-6 


84'3 


34 




26'0 


27-6 


29-6 


31-8 


34*4 


37*5 


41-2 


457 


51-4 


587 


63-2 


68-4 


74-6 


82-1 


35 


23-9 


25*3 


26-9 


28-8 


31-0 


33'5 


36-5 


40-2 


44-6 


50-1 


57-2 


61-6 


667 


72-8 


80-0 


36 


2 3'3 


247 


26-3 


28-1 


30-3 


327 


357 


39*2 


43'5 


48-9 


55-8 


60- 1 


65-1 


71-0 


78-1 


37 


227 


2 4 -I 


257 


2 7'5 


2 9'5 


32-0 


34'8 


38-3 


4 2 '5 


47-8 


54*5 


587 


63-6 


69-4 


76-3 


38 


22'2 


23-6 


25-1 


26-9 


28-9 


31*2 


34' 


37*4 


41*5 


467 


53'3 


57*4 


62-2 


67-8 


74'5 


39 


217 


23-1 


24-6 


26-3 


28-3 


30-6 


33'3 


36-6 


40-6 


457 


52-2 


56-1 


60-8 


66-3 




4 


21-3 


22-6 


24-0 


257 


277 


29*9 


32-6 


35-8 


39-8 


447 


51-1 


55-0 


59'5 


64-9 


71-4 


4 1 


20*9 


22'I 


23-6 


25*2 


27-1 


29-3 


32-0 


35'i 


39-0 


43-8 


50-0 


53'9 


58-3 


63-6 


70-0 


42 


20-4 


217 


23-1 


247 


26-6 


28-8 




34'4 


38-2 


43' 


49-1 


52-8 


57*2 


62-4 


68-6 


43 


20'I 


21-3 


227 


24-2 


26-1 


28-2 


307 


33-8 


37'5 


42-1 


48-1 


51-8 


56-1 


61-2 


67 '3 


44 


197 


2O'9 


22'2 


23-8 


25-6 


277 


30-2 


33'2 


36-8 


41-4 


47'2 


50-9 


55' 1 


60- 1 


66-1 


45 


I9-3 


20-5 


21'9 


23-4 


25-1 


27-2 


29*6 


32-6 


36-2 


40-6 


46-4 


50-0 


54-1 


59'0 


64-9 


46 


I9'O 


20'2 


21'5 


23-0 


247 


267 


29-1 


32-0 


35'5 


40*0 


45'6 


49-1 


53'2 


58-0 


63-8 


47 


187 


19-8 


21*1 


22*6 


24*3 


26-3 


287 


31*5 


35' 


39'3 


44'9 


48'3 


52-3 


57' 1 


627 


48 


l8'4 


I9-5 


20-8 


22'2 


23-9 


2 5'9 


28-2 


31*0 


34*4 


387 


44'2 


47'5 


51-5 


56-2 


6r8 


49 


18-1 


I9-2 


20-5 


21-9 


23-6 


25'5 


27-8 


3'5 


33'9 


38-1 


43'5 


46-8 


507 


55'3 


60-8 


5 


17-9 


l8'9 


20-2 


21'6 


23-2 


25-1 


27-4 


30-1 


33'4 


37'5 


42-9 


46*1 


50-0 


54'5 


59'9 


51 


17-6 


187 


I9-9 


21*3 


22'9 


24-8 


27-0 


29-6 


32-9 


37' 


42-2 


45*5 


49'2 


537 


59' i 


52 


17-4 


18-4 


19-6 


2I'O 


22-6 


24 ! 4 


26-6 


29-2 


32-5 


36-5 


417 


44-8 


48-6 




58-2 


53 


17-1 


lS'2 


19-4 


207 


22*3 


24-1 


26-2 


28-8 


32-0 


36-0 


41-1 


44-2 


47'9 


52*3 


57'5 


54 


16-9 


17-9 


I9-I 




22-0 


23-8 


25-9 


28-5 


31-6 


35'5 


40-6 


437 


47'3 


51-6 


567 


55 


167 


177 


l8'9 


20'2 


217 


23-5 


25-6 


28-1 


31-2 


35-1 


40-1 


43' 1 


467 


50-9 


56-0 


56 


16-5 


17*5 


iS-6 


19-9 


21'4 


23-2 




27-8 


30-8 


347 


39-6 


42*6 


46-2 


50-3 


55'4 


57 


16*3 




18-4 


197 


21'2 


22-9 


25-0 


27-5 


3'5 


34'3 


39' i 


42-1 


45'6 


49-8 


547 


58 


16-1 


I7*I 


18-2 




2I'O 


227 


247 


27-2 


30-2 


33'9 


387 


417 


45'i 


49*2 


54*1 


59 


16*0 


16-9 


iS-o 


19-3 


207 


22-4 


24-5 


26-9 


29-8 


33'5 


3 8 '3 


41-2 


44-6 


487 


53*5 


60 


15-8 


16-8 


17-8 


ig-I 


20'5 


22'2 


24-2 


26-6 


29-5 


33'2 


37'9 


40-8 


44-2 


48-2 


53' 


61 




16-6 


177 


l8'9 


20*3 


22'0 


24-0 


26-3 


29-2 


32-9 


37'5 


40-4 


43-8 


477 


52-5 


62 


J 5'5 


16-4 




187 


2O'I 


21'8 


237 


26-1 


29*0 


32-6 


37' 2 


40-0 


43'3 


47'3 


52-0 


63 




16-3 


71*3 


18-6 


20'0 


21-6 




25-9 


287 


3 2 '3 


36-8 


397 


42-9 


46-8 


SI'S 


6 4 


15*2 


16-1 


17-2 


18-4 


I9-8 


21'4 


23-3 


25-6 


28-4 


32-0 


36-5 


39'3 


42-6 


46-4 




65 


15-1 


16-0 


17-1 


18-2 


I9-6 


21'2 


23-1 


25-4 


28-2 


317 


36-2 


39-0 


42*2 


46-0 


50*6 


66 


15-0 


I 5*9 


16-9 


18-1 


I 9'5 


2l'I 


22-9 


25-2 


28-0 


31-5 


35'9 


387 


41-9 


457 


50-2 


67 


14-9 


15-8 


16-8 


18-0 


19*3 


20'9 


22-8 


25-0 


27-8 


31-2 


357 


38-4 


41-6 


45*3 


49'9 


68 


14-8 


157 


167 


17-8 


19-2 


207 


22-6 


24-8 


27-6 


31-0 


35'4 


38-1 


4 J '3 


45' 


49*5 


69 


147 




16-6 


177 


19-0 


20'6 


22'5 


247 


27-4 


30-8 


35'2 


37' 8 


41-0 


447 


49*2 


7 




I5'4 


16-4 


17-6 


18-9 


20-5 


22'3 


24-5 


27-2 


30-6 


34-9 


37-6 


407 


44*4 


48-8 


71 


J 4'5 




16-3 




18-8 


20-3 


22'2 


24-4 


27*0 


30-4 


347 


37*4 


40-5 


44-1 


;S'5 


/ 
72 

T\ 


14-4 
I 4'3 


i5'3 


16-3 
16-2 


17-4 


187 
18-6 


20-2 
2O'I 


22'0 
21'9 


24-2 
24-1 


26-9 
267 


30-2 
30-1 


34'5 
34*3 


36-9 


40*2 

40-1 


43*9 
43-6 


48-0 


1 3 

74 


14-2 


I 5' 1 


16-1 


17-2 


18-5 


20-0 


21-8 


24-0 


26-6 


29-9 




36-8 


39*8 


43'4 


477 


75 


14-2 


15*0 


16-0 


17*1 


18-4 


19-9 


217 


23-8 


26-5 


29-8 


34-0 


36-6 


39-6 


43'2 


47'5 


76 

77 

79 


14-1 
14-0 
14-0 
I3-9 


15-0 
14-9 
14-8 

14-8 


I5-9 

15-8 
157 


17-0 
17-0 
16-9 
16-8 


CO CO 00 00 

H to to co 


19-8 
197 
197 
I9*6 


21-6 

21-5 

21-4 

21-4 


237 
23-6 

23'5 
23-5 


26-4 
26-2 
26-1 

26'O 


29-6 

29*5 
29-4 


33-8 
337 
33-6 
33*4 


36-3 
36-1 
36-0 


39'4 
39'3 

3 g-o 


42-8 
427 
42-5 


47'3 
47-1 
46-9 
46-8 


80 




147 




16-8 


18-1 


19*5 


21-3 


23-4 


26-0 


29-2 


33'3 


35'9 


38*9 


42*4 


46-6 


81 
82 


13*9 

13-8 


147 
147 


I5'6 


167 
167 


18-0 
18-0 


I9-5 
19-4 


21*2 
21-2 


23-3 
23'3 


25-9 
25-8 


29-1 
29-0 


33'2 


35'8 
357 


387 
38-6 


42-3 
42-1 


46-5 
46-3 


83 
84 


13*8 
13-8 


14-6 
14-6 


I5-5 


167 
16-6 


17-9 
17-9 


19-4 


21' I 


23-2 
23-2 


25-8 
257 


29-0 
28-9 


33-0 


35'5 


38-6 
38'5 


42-0 
42-0 


46-2 
46' i 


85 
86 


137 


14-6 


15*5 


16-6 
16-6 


17-8 
17-8 


I9-3 

*9'3 


21*0 
21'0 


23*2 
23-1 


257 

25-6 


28-9 

28-8 


32-9 
32-9 


35'5 
35'4 


38H 


41-9 

41-8 


46-1 
46-0 


87 
88 
80 


137 
137 


*4' 
14* 


15'? 


16-6 
16-5 
16-5 


17-8 
17-8 
17-8 


I9-3 
19-2 
19-2 


21'0 
21*0 
2I'O 


23-1 
23-0 
23*0 


25-6 
25-6 
25-6 


28-8 
28-8 
287 


32-9 
32-8 
32-8 


35'4 
35'4 
35'3 


38-3 
38-3 


41-8 
41-8 
417 


46-0 
45'9 
45*9 


uy 

90 


137 


14* 


i5'5 


16-5 


17-8 


19-2 


21'0 


23-0 


25-6 


287 


32-8 


35'3 


38-3 


417 


45'9 



Table E. 

CORRECTIONS OF ALTITUDE OF THE SUN AND STARS 
(INVOLVING DIP, REFRACTION, Q's SIM JMAMETER, AND PARALLAX). 

Add the Cor. to the Alt. of the O'* Lower Limb. 



'~ < 

& 




Height of the Eye, in Feet. 


6ft. j 8ft. 

I 


10ft. 


12ft. 


14ft. 


16ft. 


18ft. 


20ft. 


22ft. 


24ft. 


1 / 


, 


j 


/ 


( 


j 


j 


j 


i 


/ 


5 1 3'9 


3*5 


3-1 


2-8 


2'5 


2'2 


1-9 


17 


I'5 


i'3 


6 j 5-2 


4-8 


4-5 


4'2 


3'9 


37 


3'4 


3 -2 


2'9 


2-7 


7 


6'4 ! 5*9 


5-6 


5'3 


5'0 


4-8 


4'5 


4'3 


4-0 


3'8 


8 


7-2 


6-8 


6'5 


6-2 


5'9 


5-6 


5'4 


5'2 


4'9 


47 


9 


7'9 


7'5 


7-2 


6-8 


6-6 


6-3 


6-1 


5-8 5-6 


5'4 


10 


8-4 


8-0 


77 


7'4 


7'i 


6-9 


6-6 


6-4 


6-2 


6-0 


ii 


8-9 


8-5 


8-2 


7'9 


7-6 


7'4 


7-1 


6-9 


6-7 


6-5 


12 


9'3 


8-9 


8-6 


8-3 


8-0 


7-8 


7'5 


7'3 


7-1 


6-9 


13 


9'6 


9-2 


8-9 


8-6 


8'4 


8-1 


7-9 


7-6 


7*4 


7-2 


J 4 


9-9 


9'5 


9-2 


8-9 


8-6 


8-4 


8-1 


7'9 


77 


7'5 


15 


I0'2 


9-8 


9'5 


9-2 


8-9 


8-6 


8-4 


8-2 


8-0 


7-8 


16 


10-4 


IO'O 


97 


9'4 


9-1 


8-9 


8-6 


8-4 


8-2 


8-0 


J 7 


io'6 


10-3 


9-9 


9-6 


9'4 


9-1 


8-9 


8-6 


8-4 


8-2 


18 


10-8 


10-4 


10-1 


9-8 


9'5 


9'3 


9-0 


8-8 


8-6 


8-4 


19 


10-9 


io-6 


10-3 


9-9 


97 


9'4 


9-2 


8-9 


87 


8-5 


20 


ii'i 


107 


10-4 


lO'I 


9'8 


9'6 


9'3 


9-1 


8-9 


8-7 


22 


11-3 


II'O 


10-7 


10-3 


IO'I 


9-8 


9-6 


9'4 


9-2 


9-0 


24 


n-6 


II-2 


io - 9 


10-6 


10-3 


IO'O 


9'8 


9-6 


9'4 


9-2 


26 


11-7 


H'4 


ill 


10-7 


10-5 


IO'2 


IO'O 


9-8 


9'5 


9'3 


28 


11-9 11-5 


II'2 


10-9 


10-6 


I0'4 


10-2 


9-9 


97 


9'5 


30 


i2'i 11-7 


II- 4 


ii'i 


10-8 


I0'5 


10-3 


IO'I 


9-9 


97 


35 


I2'4 I2'0 


II'7 


11-3 


in 


10-8 


10-6 


10-4 


lO'I 


9-9 


40 


I2'6 


I2'2 


II'9 


n-6 


11-3 


II'O 


10-8 


10-6 


10-4 


I0'2 


45 


12-8 


I2- 4 


I2'I 


n-8 


ii'5 


II-2 


II'O 


10-8 


10-5 


I0'3 


50 12-9 


I2'5 


I2'2 


11-9 


ir6 


II- 4 


II'2 


10-9 


10-7 


I0'5 


5.5 13" i 


I2'7 


I2- 4 


I2'I 


n-8 


"'5 


*3 


ii'i 


10-9 


10-7 


60 13-2 


12-8 


I2'5 


I2'2 


11-9 


n-6 


11-4 


II'2 


II'O 


10-8 


65 13-3 12-9 


12-6 


I2'3 


12-0 


n-8 


"'5 


ii'3 


II'I 


10-9 


70 13-4 13-0 


I2'7 


I2- 4 


I2'I 


11-9 


11-6 


11-4 


II'2 


II'O 


80 i3'6 13*2 


I2'9 


12-6 


I2'3 


I2'O 


n-8 


n-6 


II- 4 


H'2 


90 137 j 13-4 13-0 


I2'7 


I2'5 


I2'2 


I2'0 


11-7 


u - 5 


11-3 



CORRECTION OF A STAR'S ALTITUDE. (Subtract.) 



in 


Height of the Eye, in Feet. 


6ft. 


8ft. 


10ft. 


12ft. 


14ft. 


16ft. 


18ft. 


20ft. 


22ft. 


24ft. 


5 ! I2 '3 


i2 : 6 1 i3 ! i 


13-4 


137 


I3'9 


I 4 : 2 


i 
14-4 


I 4 ! 6 


I 4 : 8 


6 10-9 


, 


n-6 


I2'O 


I2- 3 




12-8 


13-0 


13-2 


I3'4 


7 


97 


I0'2 


10-5 


IO'9 


II'I 


ii"4 


n-6 


11-9 


I2'I 


12-3 


o 


9-0 


93 


97 


lO'O 


I0'3 


10-5 


10-8 


II'O 


II-2 


11-4 


9 


8-3 


8-7 


9-0 


9'3 


9-6 


9-8 


lO'i 10-3 


10*5 


10-7 


10 


77 


8-1 


8-4 


8-7 


9-0 


9'3 


9'5 


97 


IO'O 


IO'2 


ii 7'3 


7-6 


7*9 


8-3 


8-5 


8-8 


9-0 


9'3 


9'5 


97 


12 i 6'9 


7-2 


7'5 


7'9 


8-1 


8'4 


8-6 


8-9 


9-1 


9*3 


13 


6-5 


6-9 


7-2 


7*5 


7-8 


8-0 


8-3 


8-5 


87 


8-9 


M 


6-2 


6-6 


6-9 


7-2 


7*5 


7-8 


8-0 


8-2 




8-7 


15 


6-0 


6-3 


6-6 


7-0 


7-2 


7*5 


77 


8-0 


8-2 


8-4 


16 


5'8 


6-1 


6-4 


6-8 


7-0 


7'3 


7'5 


77 


8-0 


8-2 


17 


5'5 


5'9 


6-2 


6-5 


6-8 


7-0 


7*3 


7'5 


77 


7'9 


18 


5*4 


57 


6-0 


6-4 


6-6 


6-9 


7-1 


7*3 


7-6 


7-8 


19 


5' 2 


5*0 


5'9 


6-2 


6-5 


6-7 


7-0 


7-2 


7'4 


7-6 


20 


5' 


5'4 


57 


6-0 


6'3 


6-6 


6-8 


7-0 


7'3 


7*5 


22 


4'8 5'2 5'5 


5'8 


6-1 


6'3 


6'5 


6-8 


7-0 


7-2 


24 


4-6 i 4-9 


5'3 


5-6 


5-8 


6-1 


6-3 


6-6 


6-8 


7-0 


26 


4*4 


4-8 




5'4 


57 


5'9 


6-1 


6-4 


6-6 


6-8 


28 


4-2 


4-6 


4*9 




5'5 


57 


6-0 


6'2 


6-4 


6'6 


30 4-1 


4'4 


4-8 


5' 1 


5'3 


5;6 


5'8 6-1 


6-3 


6'5 


35 ! 3'8 


4'2 j 4'5 


4-8 






5-5 ! 5-8 


6-0 


6-2 


4 3'6 


3'9 ! 4'3 


4-6 


4-8 


5-1 


5'3 


5-6 


5-8 


6-0 


45 3'4 


3-8 4-1 


4*4 


4-6 


4'9 


5'i 


5'4 


5-6 


5'8 


50 


3'2 


3-6 


3'9 


4' 2 4'5 


47 


5' 


5'2 5'4 


5'6 


55 


3-1 


3'4 


3-8 




4'4 


4-6 


4'8 


5 * 


5'3 


5'5 


60 


3-0 


3'3 


37 


4-0 


4-2 


4'5 


47 


5'O 




5'4 


65 


2-9 


3'2 


3-6 


3'9 




4*4 




4'9 


5' r 


5'3 


70 


2-8 


3*i 


3'5 




4-0 


4'3 


4'5 


48 


5'o 




So 


2-6 


2-9 


3'3 


3'6 | 3'9 




4'3 


4-6 4-8 


5' 


GO 


2-4 


2-8 




3'4 37 


3'9 


4-2 


4-4 i 4-6 ( 4-8 



Table F. 



Acceleration. 


H. 


M. S. 


M. 


s. 


I 


o 9-86 


I 


0-16 


2 


o 19-71 


2 


'33 


3 


o 29 


57 


3 


0-49 


4 


o 39 


43 


4 


0-66 


5 


o 49-28 


5 


0-82 


6 


o 59 


14 


6 


0-98 


7 


9-00 


7 


15 


8 


18-85 


8 


'3 1 


9 


28-71 


9 


48 


10 


38- 


56 


10 


64 


ii 


48-42 


ii 


81 


12 


58-28 


12 


97 


13 


2 8 


13 


13 


2-13 


H 


2 i7'99 


14 


2-30 


15 


2 27-85 


15 


2-46 


16 


2 37' 


7 


16 


2-63 


17 


2 47 


56 


17 


279 


18 


2 57' 


42 


18 


2-96 


19 


3 T 


27 


19 


3-12 


20 


3 17 


13 


20 


3-29 


21 


3 26-99 


21 


3'45 


22 


3 36-84 


22 


3'6i 


23 


3 46-70 


2 3 


378 


24 


3 56-56 


24 


3'94 








25 


4-11 




26 


4-27 


27 


4'44 


28 


4-60 


29 


476 


30 


4'93 


31 


5-09 


32 


5-26 






33 


5'42 


Month Cor. 




34 


5'59 


to 
Sun's Alt. 




35 
36 


575 






37 


6-08 




Jan. 4-0-3 




38 
39 


6-24 
6-40 


Feb. -f 0-2 




40 


6-57 


Mar. + 0-1 






674 


April o-i 
May 0-2 




42 
43 
44 


6-90 
7-06 


June o - 2 




45 


7'39 


July -0-3 




46 


7'56 


Aug. - 0-2 
Sep. o-i 




47 
48 

49 


772 
7-89 
8-05 


Oct. +0-1 




50 


8-21 


Nov. 4- 0-2 




51 


8-38 


Dec. 4- 0-3 




52 
53 


8-54 
8-71 






v v / 

55 9-04 






56 9-20 






57 9'36 






58 9'53 






59 ; 9 69 






60 9 86 



87 



Table E. 

CORRECTIONS OP ALTITUDE OF THE SUN AND STARS 
(INVOLVING DIP, REFRACTION, O'* SEMIDIAMETER, AND PARALLAX). 

Add the Cor. to the Alt. of the O'* Lower Limb, except where marked (minus). 



SUPPLEMENTARY TABLES 
FOR LOW ALTITUDES. 



jj 


Height of the Eye, in Feet. 


26ft. 28ft. 


30ft. 


35ft. 


40ft. 


45ft. 


50ft. 


55ft. 


60ft. 


70ft. 


80ft. 


o 


j 


( 


t 


t 


, 


, 


/ 


t 


/ : , 


, 


5 


I'l 


0-9 


0-7 


'3 


O'l 


-0'5 


-0-8 


I'2 


-1-6-2-8 


-3'3 


6 


2 '5 


2-4 


2'2 


1*7 


1-3 


0-9 


0-6 


O'2 


-o-i -0-7 




7 


3-6 


3'5 


3'3 


2-8 


2*4 


2'I 


1/7 


i'3 


I'O' O'4 -0'2 


8 
9 


4'5 


4'3 


4 '2 

4-8 


37 
4'4 


3'3 3'0 
4-0 3'6 


2'6 

3'3 


2'2 


1-9; i'3 0-7 

2'6 2'0 I'4 


10 


5'8 


5-6 


5-4 


5-0 


4 '6j 4-2 




3*5 


3 -2 2-5! 2'0 


ii 


6-3 


6-1 


5'9 


5'5 


5'0 47 


4'3 


4-0 


3-6 3-0 2-5 


12 


6-7 


6-5 


6-3 


5'9i 5'5i 5'i 


47 


4'4 


4'i 


3'5i 2-9 


13 


7-0 


6-8 


6-6 


6'2| 5'8 


5'4 


5-1 


47 


4'4 


3'8 


3-2 


14 


7'3 


7-1 6-9 


6'5 


6'i 


57 


5'4 




47 


4-1 


3'5 


15 


7-6 


7'4 


7-2 


6-8 


6' 4 


6-0 


5-6 


5'3 




4'4 




16 


7'8 


7-6 


7'4 


7-0 


6-6 


6'2 


5'9 


5'5 


5' 2 


4-6 


4-0 


17 


8-0 




7-6 


7-2 


6'8 


6-4 


6-1 


57 


5'4 


4-8 




18 


8'2 


8-0 


7-8 




7-0 


6'6 


6'3i 5'9 


5-6 


5'o 


4'4 


19 


8; 3 


8'2 


8-0 


7'5 




6-8 




6'i 


5'8 


5'i 


4-6 


20 




83 


8-1 


77 


7'3 


6-9 


6'5 


6-2 


5'9 


5'3 


47 


22 


8-7 


8-6 


8-4 


7'9 


7'5 


7-2 


6'8| 6-5 


6'2 


5'5 




24 


9-0 


8-8 


8-6 


8'2 


7-8 


7-4 7-0 6-7 


6-4 


5-8 


5' 2 


26 


9-1 


9-0 


8-8 


8'3 


7'9 


7-6 


7-2 


6-9 


6'6 


5'9 


5'4 


28 


9'3 


9-1 


8-9 




8'i 


77 


7'4 


7-0 6' 7 


6'i 


5'5 


30 


9'5 


9'3 


9-1 


8-7 


8'3 


7'9 


7'5 


7-2 


6-9 


6-3 


57 


35 


97 


9-6 9-4 


8-9 


8' 5 


8-2 


7'8 


7'5 


7-2 


6-5 


6-0 


40 


I0'0 


9-8 9-6 


9-2 


8-8 


8-4 


8-0 7-7 


7'4 


6-8! 6-2 


45 


IO'I 


lO'O: 9'8 


9'4 


9-0 


8-6 


8-2 7-9 


7-6 


7-0 


6-4 


50 


10-3 


io'i| 9-9 


9'5 


9-1 


8-7 


8- 4; 8-0 


77 




6-5 


55 




10-3 10 i 9-7 


9'3 


8-9 


8'5; 8-2 


7'9 


7'3 


6-7 


60 


io'6 


IO'4 IO 2 


9-8 


9'4 


9-0 


8-6 


8-3 


8-0 


7'4 


6-8 


65 10-7 


10-5 


io'3 


9-9 


9'5 


9-1 


87 


8-4 


8'i 


7'5 


6-9 


70 


10-8 


io'6 


10-4 


lO'O 


9-6 


9-2 


8'8 


8-5! 8-2 


7-6 


7-0 


80 


iro 


10-8 


io'6 


IO'2 


9-8 


9'4 


9-0 


8-7 8-4 


7-8 


7-2 


90 


II-I| IO-Q 


10-8 


10-3 


9-9 


9-6 


9-2 


8-9 8-5 


7'9 


7'4 



CORRECTION OF A STAR'S ALTITUDE. (Subtract.) 



^ Height of the Eye, in Feet. 


| 


26ft. 


28ft. 


30ft. 


35ft. 


40ft. 


45ft. 


50ft. 


55ft. 


60ft. 


70ft. 


80 it. 


| ' 

5 T 5 c 


15-2 


J 5'4 


15-8 


16-3 16-6 


17-0 


17-4 


17-7 i8'4J 18-9 


6 13-6 


13-8 


14-0 


14-4 


14-8 


15-2 


15-6 


I5-9 


16-3 


16-9! 17-5 


7 I2 '5 


I2'7 


12-9 


I3-3 


137 


14-1 


14-6 


14-8 


15-1 


15-8 


16-3 


8 n-6 


ii'8 


I2'0 


12-4 


I2'8 


13-2 


13-6 13-9 


14-3 


14-9 


15-4 


9 i 10-9 ii'i 


ii'3 


11-7 


I2'I 


12-5 


12-9 


13-2 


13-5 


14-2 


M7 


IO 


10-4! 10-6' 10-7 




n-6 


11-9 


12-3 


I2'6 


13-0 


13-6 


14-2 


ii 


9-9! io-i 


10-3 


10-7 


ii'i 


n'5 


H'9 I2'2 


12-5 


13-1 


T 37 


12 


9'5 97 


9-8 


10-3 


10-7 


II'O 


11-4 n-8 


I2'I 


12-7 


I3-3 


13 


9-1 


9'3 


9'5 


9-9 


10-3 


10-7 


in n-4 


117 


12-3 


12-9 


H 


8-9 


9-0 


9-2 


97 


IO'I 


10-4 


10-8 ii'i 


11*4 


I2"I 


12-6 


15 


8-6 


8-8 


8-9 


9'4 


9-8 


IO'I 


10-5 i0'8 




n-8 


12-3 


16 


8-4 


8-5 


87 


9-2 


9'6 


9-9 


10-3] io'6 


io'9 


n-6 


I2'I 


I 7 




8'3 


8'5 


8-9 


9'3 


97 


lo'il 10-4 


id- 7 11-4 


II'9 


18 i 7-9 


8-1 


8'3 


8'8 


9-2 


9'5 


9-9 10-2 


10-5 


II-2 


11-7 


19 7-8 


8-0 


8-2 


8-6 


9-0 


9'4 


97 I0>1 


10-4 


II'O 


n-6 


20 : 7'7 


7-8 


8-0 


8-5 


8-9 


9-2 


9-6 9-9 


I0'2 


10-9 


11-4 


22 j 7-4 


7-6 


7-8 


8-2 


8-6 


9-0 


9'3 


97 


io'O io'6 


II'2 


24 


7-2 


7'4 


7'5 


8-0 


8-4 


8-7 


9-1 


9'4 


9'8! 10-4 


iO"9 


26 


7-0 


7-2 


7'4 


7-8 


8'2 


8'6 


8-9 


9'3 


9 4 6 I0'2 


10-8 


28 


6-8 


7-0 


7-2 


7-6 


8-0 


8-4 


8'8 


9'i 


9'4 


I0'0 


io-6 


30 6'7 


6-9 


7-0 


7'5 


7'9 


8'2 


8'6 


8-9 


9'3 


9-9 


10-4 


35 i 6-4 


6-6 


6-8 


7-2 


7-6 


8-0 


8'3 


8-7 


9-0 


9-6 


I0'2 


40 ! 6-2 


6' 4 


6-5 


7-0 


7'4 


77 


8'i 


8-4 8-8 


9'4 


9-9 


45 6'o 


6'2 


6' 4 


6-8 


7-2 


7-6 7-9 


8-3 8-6 


9-2 


9'8 


50 


5-8 


6-0 


6'2 


6'6 


7-0 


7'4 7' 8 


8'i 8' 4 


9-0 


9-6 


55 


57 


5'9 


6"! 


6'5 


6-9 7-3 7-6 


7'9 8-3 


8-9 


9'5 


60 


5-6 


5-8 


5-9 


6- 4 


6-8 7-1 7-5 


7-8 8-2 


8-8 


9'3 


65 


5-5 


57 






67 7'0 7'4 


77i 8-i 


87 


9'2 


70 


5'4 


5-6 


57 


6'2 


6-6' 6-9 7-3 


7-6: 8-0 


8-6 


9-1 


80 


s;2 


5'4 




6-0 


6-4 6-8 7-1 


7'5 7' 8 | 8-4 


9-0 


90 




5'2 


5'4 


V8 


6-2| 6'6 ! 6-9 


7'3 7'6| 8 '2 


8-8 



Correction for Small Altitudes. 


I* 


*! 


2nd Correction, 
Various Heights. 


u 



M 


\Add to] 


JP 


O 


~~ ! Subt. \% 




32 




from ) 


o / 


j 


Ft. 


t 


3 o 


-4'9 


6 


+ 3-8 


3 10 


4*4 


8 


3'4 


3 20 


3*9 


10 


3'i 


3 30 


3'4 


12 


2-8 


3 40 


3-0 


M 


2'5 


3 5 2-5 


16 


2-3 


4 o 


2'I 


18 


2'I 


4 10 


1-8 


20 


r8 


4 20 


i'4 


22 


1-6 


4 30 


I'O 


24 


*'4 


4 40 


0-8 


26 


I'2 


5 o 


0-2 


28 


I'O 


5 20 


+ 0-4 


30 


0-8 


5 40 


0-9 


32 


07 


6 o 


1*3 


34 


'5 


6 20 


i'7 


36 ! 0-3 


6 40 


2'I 


38 0-2 


7 o 


2'4 


40 : o-o 


7 20 


27 


42 | 0'2 


7 40 


3 -0 


44 0-3 


8 o 


3*3 


46 , 0-5 


8 20 


3*5 


48 0-6 


8 40 


3-8 


50 07 


8 50 


3*9 


52 : 0'9 


9 o 


4-0 


54 i'o 


9 20 


4-2 


56 


ri 


9 4 


4'4 


60 


i'4 


IO O 


4-6 


65 


17 


10 30 


4-8 


70 


2'0 


II 


5'o 


75 


2'3 



Star's 
Altitude. 


d 

3 

ja 
be 
' 

a 


2nd Correction, 
Various Heights. 


- 


Add to] j 

Suft*. f< 
from J 


* 


( 


Ft. 




3 o 


21*1 


6 


+ 3-3 


3 10 


20'6 


8 


3'4 


3 20 


20'0 


IO 


3-1 


3 30 


I9'5 


12 


2'8 


3 4 


19-1 


*4 


2-5 


3 50 


187 


16 


2-3 


4 o 


18-3 


18 


2'I 


4 10 


17-9 


20 


1-8 


4 20 


J 7'5 


22 


r6 


4 30 


17-2 


24 


i'4 


4 40 


16-9 


26 


I'2 


5 o 


16-3 


28 


t*O 


5 20 


15-3 


3 


0-8 


5 40 


I5-3 


32 


0-7 


6 o 


14-8 


34 


o'5 


6 20 


14-4 


36 


0-3 


6 40 


14-1 


38 


0'2 


7 o 


137 


40 I o-o 


7 20 


I3'4 


42 0-2 


7 4 


U' 1 


44 0'3 


8 o 


12-8 


46 


0'5 


8 20 


12-6 


48 


0-6 


8 40 


12-4 


5 


07 


8 50 


12-3 


52 


0-9 


9 o 


I2'I 


54 


I'O 


9 20 


irg 


56 


I'l 


9 4 


11-7 


60 


I- 4 


IO 


ir6 


65 


17 


10 30 


11-3 


70 


2-0 


II O 


in 


75 


2'3 



88 

Table G. 
STAR POLARIS AZIMUTH TABLE. 



*'s Hr. 
Angle. 


LATITUDES. 


*'s Hr. 
Angle. 





10 


20 


30 


35 


40 


45 


50 


55 C 


80 


AZIMUTHS. 


H. M. 

















o 


o 











H. M. 


o oo 


O'O 


O'O 


O'O 


O'O 


O'O 


O'O 


O'O 


O'O 


O'O 


O'O 


12 OO 


o 20 


O'l 


O'l 


O'l 


O'l 


O'l 


O'l 


O'l 


O'2 


O'2 


O'2 


II 40 


o 40 


0'2 


0-2 


O'2 


O'2 


0-3 


0-3 


0-3 


0-3 


0-4 


0- 4 


II 2O 


I OO 


0'3 


0'3 


0'3 


*4 


0-4 


0-4 


0-4 


o'5 


0-5 


0-6 


II OO 


I 20 


0-4 


0- 4 


0'4 


o'5 


0'5 


o'5 


0-6 


0-6 


07 


0-8 


10 40 


I 40 


0'5 


0'5 


0'5 


0-6 


0-6 


07 


07 


0-8 


0-9 


I'O 


10 2O 


2 OO 


0-6 


0-6 


0-6 


07 


07 


0-8 


0-8 


0-9 


i 


'2 


IO OO 


2 20 


07 


07 


07 


0-8 


0-8 


0-9 


I'O 


I'O 


'2 


'4 


9 40 


2 40 


0-8 


0-8 


0-8 


0-9 


0-9 


I'O 


i'i 


I'2 


3 


6 


9 20 


3 oo 


0-8 


0-8 


0-9 


o 


I'O 


i'i 


I'2 


i'3 


'5 


7 


9 oo 


3 20 


0-9 


0-9 


I'O 


o 


i 


1'2 


i*3 


1-4 


6 


8 


8 40 


3 40 


I'O 


I'O 


I'O 


I 


2 


i'3 


i'4 


1*5 


'7 


2'0 


8 20 


4 oo 


I'O 


I'O 


I'l 


'2 


'2 


i'3 


i'5 


1-6 . 


8 


2'I 


8 oo 


4 20 


I 


I'l 


I'l 


'2 


'3 


J '4 


i'5 


17 


9 


2'2 


7 40 


4 40 


I 


I'l 


I'2 


3 


'4 


i'4 


1-6 


17 


9 


2'2 


7 20 


5 oo 


I 


I'2 


I'2 


3 


i'4 


i'5 


1-6 


1-8 


2-0 


2' 3 


7 oo 


5 20 


"2 


1*2 


I'2 


'3 


i'4 


i'5 


1-6 


i-8 


2'0 


2-3 


6 40 


5 40 


2 


I'2 


1*2 


'4 


J< 4 


i*5 


17 


i-8 


2'0 


2'3 


6 20 


6 oo 


2 


I'2 


I'2 


'4 


i'4 


i'5 


17 


i-8 


2'0 


2' 4 


6 oo 



For the twelve hours before the meridian passage (above the Pole) it is east of north, and 
for the twelve hours after it is west of north. 

DIAGRAM to illustrate the Apparent Motion of Star a Ursae Minoris (Polaris) round the Pole, 
Declination of Star in 1910, 88 49^' N. ; Right Ascension, ih. 27m. 



OOHrs. 



3Hrs 



6Hrs 




/5/frs. 



I2tfrs. 



89 
REDUCTION TO THE MERIDIAN TABLE FOR * POLARIS. 



AT HOUR-ANGLES FROM UPPER MERIDIAN. 

Add Reduction to obtain Meridian Altitude. 



AT HOUR-ANGLES FROM LOWER MERIDIAN. 

Subtract Reduction to obtain Meridian Altitude. 



"&c 
a 

ri 


LATITUDES. 


1 


10 


20 


30 


40 j 50 60 


E 








Oio 


O'l 


O'l 


O'l 


O'l 


O'l 


O'l 


20 


O'3 


O'3 


0-3 


O'3 


0-3 


0-3 


30 


0-6 


0'6 


0-6 


0-6 


0-6 


0-6 


40 












IBM 


5 










2- 


7 
2'5 


IO 


3'3 


3*3 


3'3 3'3 


3-3 


3'4 


20 


4'3 


4'3 


4'3 4'3 


4'4 


4'4 


3 


5'4 


5'4 


5'4 5'4 


5'5 


5'5 


40 


6'6 


6-6 


67 


67 


67 


6'8 


50 


8-0 


8-0 


8-0 


8-0 


8'i 


8'2 


II o 


9'5 


9'5 


9'5 


9-6 


97 


9'8 


IO 


II'O 


ii'i 


II'2 


II'2 


11-3 


11-4 


20 


I2'8 


I2'8 


12-9 


12-9 


13-0 


13-2 


30 


14-6 


14-6 


J 47 


I4'8 14-9 


15-0 


40 


16-5 


16-6 


167 


16-7 i6'8 


17-0 


50 


18-6 


18-6 


187 


18-8 


18-9 19-1 


III 


207 


20'8 


20'8 


20-9 


21*1 


21-3 


10 


22'9 


23-0 


23-1 


23'2 


23-3 


2 3'5 


20 


25-2 


25-3 


25-4 


2 5'5 


257 


2 5'9 


30 


2 7 '6 


277 


27-8 


27-9 


28'I 


28-4 


40 


30-1 


30-2 


30-3 


30-4 


3O'6 


30-9 


50 


327 


32-8 


32-9 


33'0 


33' 2 


33'5 


IV o 


35'3 


35'4 


35-5 


357 


35'9 


36-2 


10 


38-0 


38-1 


38-2 




38-6 


38-9 


20 


40-8 


40-9 


41-0 


41-2 


41-4 


417 


30 


43-6 


437 


43'9 44'0 


44-2 


44-6 


40 




46-6 


467 46-9 


47 -I 


47'4 


50 


49'4 


49'5 


49-6 49-8 


50-1 


50-4 


V o 


52-3 


52-4 


52-6 52-8 


53-0 


53'3 


IO 


55'3 


55'4 


55'6 55-8 


56-0 


56'3 


20 


58-3 


58-5 


58-6 


58-8 


59'o 


59'4 


30 


i 1-4 




i 17 


i 1-8 


I 2'I 


I 2'5 


40 


i 4-4 


i 4'5 


i 471 4-9 


i 5-1 


i 5'5 


50 


i 7'5 


i 7-6 


i 7-81 8-0 


I 8'2 


i 8-6 


VI o 


i iO'6 


i 107 


i io'8 i ii'o 


i 11-3 


i ii'7 



i 



O'O 

O'l 
O'l 
0'2 
0'2 

0-3 

0-3 
0-4 

0-5 
0-5 
0-7 
07 

0-8 
0-9 

I'O 

I'l 



1-6 
1-7 
1-9 

2'0 
2'I 

2'2 

2-4 

2'5 

2-6 

2'8 

2-9 








mt 

c 
? 


LATITUDES. 


3 

o 


10 1 20 


30 


40 


50 


60 


tr! 










H. M. 


o < 


/ 


/ 


1 


/ 


/ 


10 


O'l 


O'l 


O'l 


C'l 


O'l 


O'l 


20 


o'3 


0-3 


O'3 


o'3 


o'3 


0-3 


30 o - 6 


0-6 


0-6 


0-6 


0-6 


0-6 


40 ri 


i'i 


i'i 


i'i 


i'i 


I'O 


50 17 


17 


17 


17 


17 


1-6 


1 o 2-4 


2-4 


2-4 


2-4 


2-3 


2-3 


IO 

20 


3'3 3'2 


3-2 




3-2 


3'i 


30 


5'3 5'3 


5'3 


5-3 


5'2 


5'2 


40 


6-6 


6'6 


o' 5 




6-4 


6-4 


50 


7'9 


7'9 


7-9 


7-8 


7-8 


77 


II o 


9'4 


9'4 


9-3 


9'3 


9-2 


9-1 


IO 


II'O 


io'9 


10-9 


10-9 


10-8 


107 


20 


127 


I2'6 


I2'6 


12-5 


12-5 


12-3 


30 


I 4'5 


I 4'5 


14-4 


I 4'3 


14-2 


14-1 


40 


16-4 


16-4 


16-3 


16-2 


16-1 


i6'o 


50 


18-5 


18-4 


18-3 


l8'2 


18-1 


18-0 


III 


2O'6 


20-5 


20-4 


20'3 


2O'2 


20'0 


10 


22'8 


227 


22'6 


22'5 


22' 4 


32'2 


20 


25'I 


25-0 


2 4 '9 


24'8 


247 


24^ 


30 


2 7'5 


27-4 


2 7'3 


27'2 


27'0 


26'8 


40 


29-9 


29-9 


29-8 


29'6 




29'2 


50 


32-5 


32-4 


32-3 


3 2'2 


32-0 


3*7 


IV o 


35'i 


35-0 


34'9 


34-8 


34 ;6 


34'3 


10 


37-8 


377 


37-6 


37'4 




36-9 


20 


40-6 


40-5 


40-3 


40-2 


40-0 


397 


30 


43'4 


43'3 


43'i 


43' 


42-8 


42-4 


40 


46-2 


46-1 


46*0 


45-8 




45'2 


50 


49-1 


49-0 


48-9 


487 


48-5 


48-1 


V o 


52-1 


52-0 


51-8 


51-6 


51-4 


51-0 


IO 




54'9 


54-8 


54-6 


54'4 




20 


58-1 


58-0 


57-8 


57-6 


57'4 


57-0 


3 




I I'O 


i 0-8 


i 0-6 


i 0-4 


I O'O 


40 


I 4 '2 


i 4-0 


i 3'9 


i 37 


i 3'4 


i 3-1 


50 


i 7-2 


i 7-1 


i 7-0 


i 6'8 


i 6-5 


i 6'i 


VI o 


i 10-3 


I IO'2 


I IO'O 


i 9-8 


i 9-6 


i 9-2 



For Azimuths of # Polaris see page 88. 

EXAMPLES IN THE USE OF THE ABOVE TABLE. 

Example i. On April 2nd, 1914, at 3h. 30 m. a.m., A.T. Sp. in latitude by D.R. 40 15' N., 
longitude 11 W. Required the approximate altitude of Polaris for setting the sextant for an 
observation to obtain the latitude. Height of eye, 40 ft. 

H. M 



Mer. pass of # in 1910 (p. 10) o 44 a.m. below Pole. 
Cor. for 4 years (see p. 6) +2 


Lat. by D.R. 
P.D. of * 

Mer. alt. 
40 ft. cor. (p. 87) 

Reduction 
Alt. for sextant 


40 15 N. 

-I 9'2 


*'s Dl. 88 50-8 N. 
90 o'o 


Mer. pass, in 1914 o 46 a.m. 
Time at ship 3 3 a.m. 

K'sApprox. H.A. (below Pole) 2 44 gives reduction 167. 

H. M. , , M. , 

Reduction at 2 40 = i6'2 '2x4 = + '8 
Cor. + '5 7 x -4 var in 4 years = - '3 


39 5'8 

+ 7'5 

39 i3'3 

+ 167 


P.D. i 9-2 N. 


39 30 N. 


. 


True reduction 167 + '5 



Example 2. On April 2nd, 1914, at 3h. 3501. a.m., A.T. Sp. in latitude by D.R. 40 15' N., 
longitude 11 W. Observed altitude of # Polaris was found to be 39 40' N. Height of eye, 37ft. 
Required the latitude. 



Obsd. alt. of * 39 40 N. 

Eye, 4oft. (cor. p. 87) - 7'5 



Mer. pass, of # in 1914 
Time of observation 



H. M. 

o 46 a.m. 
3 35 a.m. 



Reduction 

Mer. alt. (below Pole) 
P. dist. in 1914 

Latitude 



Reduction i8'o 

Cor. for 4 years '3 

#'s Approx. H.A. (below Pole) 2 49 gives reduction 177. True reduction 177 



*'s Sidereal H.A. would be nearly i m. greater ; this correction, if required, 
may be made from the acceleration table, (page 86). It will be nearly i m. 
40 24'o N. greater for 6 hours. 



90 



DIAGRAM TO AID IN FINDING THE. POSITION OF SOUTH POLE. 

This diagram represents the apparent motion of the bright high-declination stars 
Achernar, Canopus, and those in the constellations of the Southern Cross and Centaurs 
to an observer in the latitude of Wellington, New Zealand, in about 41 S. In this 
latitude none of these stars ever set, and they appear to describe a circle round an 
imaginary South Pole, with a radius equal to the co-declination of the star. The radius 
of a Crucis, for instance, is about 27^. It will be seen from the diagram that Cen- 
tauri and Achernar are always on opposite sides of the circle to one another, and 
that both stars are at nearly equal distances from the Pole ; therefore the approximate 
position of the South Pole in the heavens will always be at a point midway between 
these two stars. When ft Centauri is on the meridian above the Pole, Achernar will 
be close to the meridian below the Pole, or when ft Centauri is east of the Pole 
Achernar will be about the same distance west of the Pole. The Centaurs will appear 
in almost exactly the same position in the heavens at, say, 6 p.m. on any given day that 
Achernar was in at 6 a.m. on the same day, or the Centaurs will appear in almost 
exactly the same position at 6 p.m. on one day that Achernar was in at the same hour 
of the day six months previously. 




91 

GENERAL REMARKS. RULES, AND EXAMPLES, 




GENERAL* REMARKS ON THE DOUBLE-ALTITUDE AND "SUMNER" 

PROBLEM. 

Many navigators undervalue " Sumner's " method in low latitudes ; first, 
because of the small change of bearing between the usual times of taking the 
observations, and, secondly, because with a high altitude the circle of altitude or 
line of position is not to the ;same extent a straight line on the chart. But in 
practice I have found " Sumner's " method give equally good, or better results in 
low latitudes than in high, if the observations are taken or, at any rate, the second 
one is taken within an hour of noon, or considerably less than an hour when in 
the tropics and latitude and declination are of the same name, in which case the 
" Sumner " or double-altitude method is all the more valuable, as an ex-meridian 
of the sun by itself would not give a dependable latitude unless the observation 
was taken within a very few minutes from noon ; whereas in high latitudes an 
ex-meridian will often give a latitude fairly near the truth when the observation 
has been taken nearly an hour from the meridian. In low latitudes, when observa- 
tions are taken on both sides of the meridian, 90 change of bearing may o'ften 
be obtained within an hour, and by the aid of Blackburne's and Westland's ex- 
meridian tables a good " Sumner " position may be very quickly and accurately 
obtained from ex-meridian east and west of the meridian. To illustrate this an 
extreme case is given in this work where the greater altitude is- 89, and the change 
in bearing in 5 m. amounted to 72. 

It is impressed on navigators in these pages by the numerous examples and 
illustrations following that the lines of position need never be of great length, so 
that they may always be considered as straight lines even in tropical latitudes. 
When D.R. latitude is very uncertain, and one of the observations has been taken 
anywhere near the meridian, it may be worked out as an ex-meridian, plotted on 
the chart, and combined with another observation taken nearer the prime vertical, 
which would be worked out for a longitude ; or two ex-meridian observations may be 
be taken and plotted on the chart, examples of which are given on pp. 152 and 
153. Reviewers of former editions of this work have been much struck with the 
simplicity and practical value of this problem. Although the work is simplified 
and graphically illustrated by plotting the latitudes or longitudes on the chart, the 
resulting position is readily obtained by calculation without the aid of chart, as 
shown on pp. 92 to 95. 

As most ex-meridian tables and methods of calculation only give a correct latitude 
when the observation is taken not far from the meridian, a method is given in this work 
\vhich gives a correct latitude corresponding to a given hour-angle when the sun or 
other celestial body is several hours away from the meridian. The D.R. latitude is not 
used in this calculation. 

In obtaining the latitude by the double-altitude or " Sumner " method it is best, if 
the observations are taken on the same side of the meridian, for the same person to 
observe both ; and generally the truest latitude will be found if both observations are 
taken on the same side bf the meridian, as it is probable that, if for any reason the 
altitude is observed too high or too low, the same thing will occur in both observations. 
For the same reason the truest longitude will be found from observations taken on different 
sides of the meridian. An example to illustrate this is given on pp. 114 and 115. 

REMARKS ON P.M. OBSERVATIONS. 

Any one who is in the habit of regularly taking p.m. sights must have noticed 
the large differences which sometimes occur between a.m. and p.m. observa- 
tions, which is generally attributed to current, and some men have even been led 
to believe from this that p.m. sights are not of any value, as though the sun or, 
rather, the earth did not move as uniformly in the afternoon as in the forenoon. The 
principal difference between the result of the two observations is probably generally due 
to erroneous altitude, especially in rough weather, and sometimes, of course, to erroneous 
latitude, and the mean of the results from the two observations will generally be nearest 
the true position. It has often been noticed when there is a heavy sea on that p.m. 
sights place the longitude a long way to the eastward of the a.m. ones, owing probably 
to the sun being observed on the top of a wave, and consequently, the altitude being 
too small, an error which in the morning would place the ship to the westward of the 



92 

true position, but in the afternoon just as much to the eastward of it ; so that, suppos- 
ing the ship to be in latitude 48 and the sun to be 30 from meridian at each observa- 
tion, an error in the latitude of 2' too little on both occasions would make a difference of 
12' of longitude, as may be seen from Table D, on p. 80. Suppose, then, that on the same 
occasion both observations have been worked with an error of 2' south of the true 
latitude ; this would make another difference of about ioA' of longitude, making the 
p.m. sights 22%' of longitude to eastward of the a.m. observation, and a slight easterly 
current in the interval between the two observations might easily make over 30' 
difference. Generally, no doubt, one of these errors will in a measure counteract 
another, but exceptional occasions are almost sure to arise when they will all combine 
in the same direction. 



RULE FOR FINDING THE POSITION OF SHIP FROM TWO OBSERVA- 
TIONS BY AID OF TABLES A, B, AND C 2 WITHOUT THE USE OF 
. CHART. 

FROM Two CHRONOMETER OBSERVATIONS OF THE SUN. 

(i.) Let two chronometer observations be taken at an interval of about an hour 
and a half or two hours,* and let the first be worked out with the D.R. latitude at 
the time of observation. 

(2.) Let the D.R. latitude and longitude thus obtained be corrected for the run 
of the ship in the interval between the observations, and let the second observation be 
worked with the corrected latitude. Name these longitudes (i) and (2). 

(2.) With the hour-angle, latitude, and declination at each observation, take out the 
difference of longitude correction from Tables A and B, and name the position-lines 
corresponding to these corrections according to the instruction under the heading of 
Table C 2 (p. 75). 

Tables A B give the error in longitude due to i' of error in latitude. 

When both Position-lines go through the Same or Opposite Quadrants. 

(3.) The difference between the two A and B corrections will give the difference in 
the resulting longitudes due to i' of error in the latitude. (See example on p. 100.) 

When both Position-lines go through Adjacent Quadrants. 

(4.) The sum of the two A and B corrections will give the difference in the resulting 
longitudes due to i' of error in the latitude. (See example on pp. 102 and 107.) 

The three elements used in the calculation of time, or longitude, are altitude, 
latitude, and polar distance. Presuming that the altitude and polar distance 
are correct, the resulting difference in longitude between the two observations 
must be due to error in the latitude. The sum or difference of the two A and B 
corrections give the difference of longitude in the two observations due to i' of 
error in the latitude used in the calculation, and the amount of error in the latitude 
will therefore be found by a simple proportion sum (see p. 100) from which it will 
be seen that the error or correction to be applied to the D.R. latitude will be found 
by dividing the difference between longitudes (i) and (2) by the sum or difference 
of the A and B corrections. It must be applied to the latitude used in the last 
observation, and to the N. or S. according to whether the position-lines cut one 
another N. or S. of the D.R. latitude used in the calculation. The true longitude 
is then found by multiplying either of the A and B corrections by the latitude 
error, and applying the correction according to the trend of the position-line. 

To prevent the possibility of making a mistake in the application of the correc- 
tion to the latitude, a short horizontal line representing the parallel of D.R. latitude 
may be drawn with a free hand in the work-book ; on this line put down longitudes 
(i) and (2), and roughly draw the position-lines through each longitude, following 
the rule for naming the position-lines given on p. 75, under the heading of Table C 2 , 
also bearing in mind that if the line runs in a north-easterly direction it is equally 

* Provided the sun's bearing has changed not less than two point?. 



93 

true that the line must also run in the opposite direction or south-westerly. No 
scale for longitude need be used, or protractor for laying down the bearings, but 
simply put longitude (i) or (2) to the right or left of the other, as they are to the 
east or west of one another, then draw the general trend of the position-lines through 
these^two longitudes, thus : 




( i) 




in 



FOR STELLAR OBSERVATIONS. 

When finding the position of ship from stellar observations, it is best to observe 
the altitude of two stars which have a considerable difference in bearing from one 
another, and to take both observations within a few minutes of the same time. If the 
ship has not appreciably changed her position during the interval between the obser- 
vations, both observations may be worked with the same latitude, and no correction 
for run need be applied to the first-observation latitude or longitude. Otherwise the 
same rules apply as for the observations by the sun. 

When the ship has appreciably changed her position during the interval between 
the observations, rules Nos. i and 2 must be observed as in the sun observations. 



FROM EX-MERIDIAN AND CHRONOMETER OBSERVATION COMBINED. 2B?C 

Let two observations be taken with a suitable difference in bearing between them , 
and let the one nearest the prime vertical be used for a longitude (working it with the 
D.R. latitude), and the other one for a latitude, using the time deduced from the 
longitude found by observation in the calculation for latitude : bring both results up to 
the same instant of time by applying the run in interval between the observations. 

Take out the A and B correction for the H. A. and latitude of each observation, and 
with this enter Table C 2 (p. 75) and take out the corresponding position-lines. We have 
then two latitudes and their corresponding position-lines starting from different points 
on the same meridian. Where these lines cut with one another on a plane chart will be 
the position of the ship. 

From the figure representing these posi- 
tions and position-lines it will be easy for any 

A / <p/n'<? one having a knowledge of plane trigonometry 

/743O'. to com plete the calculation. For the sake of 

those who have not this knowledge, examples 
taken from the problems given in this book are 
now given to illustrate the different cases. 



EXAMPLE i (p. 109). Observations East and 
\Vest of Meridian. 

With lat. 41 o' S., long, by chron. from 
* Canopus gave 174 30' E. and position-line 
S. 44iE. 

With long. 174 30' E., lat. by ex-mer. of 
* a Centauri gave 41 26' 40'' S. and position - 
line N. 61 E. 

For the figure. From A, in lat. 41 o' S. and 
long. 174 30' E., draw a meridian-line to B, in 
lat. 41 26' 40" S. ; from A and B draw the 
lines S. 44^ E. and N. 61 E. respectively to 
cut one another at C. From C drop a perp. 
on A B at D. 

In the right angled triangles ADC and BDC 
the angles at C will be respectively 45^ and 29 , 
and therefore the angle at C in the A A B C 
will = 74$. We then have in the A ABC, 
A = 44^, C - 74^, and AB = 267. First 
find a, then BD, and next CD. 




94 

Formula. 

a = A B sin A cosec C 
B D = a ' cos B 
C D = a cos C. 



Cor. for lat. 



AB 

B 

C 



B 
BD 



267' 

44i 
74i 



19-42' 
29 



Cor. for long. C D 17-0' 



Log 1-4265 
Sin 9-8457 
Cosec 0-0161 



Log 
Cos 



Log 
Cos 



1-2883 
9-6856 



Log 0-9739 



1-2883 
9-9418 



Log 1-2301 



Lat. by ex-mer. 41 26 40 S 
Cor. 9 25 N 

Correct lat. 41 17 17 S 



Long, by chron. 174 30 E 
Cor. 17 E 

Correct long. 174 47 E 



FROM Two EX-MERIDIAN OBSERVATIONS ON DIFFERENT SIDES OF THE 

MERIDIAN. 

Let two observations be taken with a suitable difference in bearing between 
them, one east and the other west of the meridian, deducing the hour-angle by 
applying the equation of time and longitude by D.R. Bring both results up to 
the same instant of time by applying the run in interval between the observations. 
The latitude from either observation (if worked by a correct method) is the latitude 
where the circle of altitude of the body observed cuts the meridian used in deducing 
the time. If both latitudes agree when observations have a considerable difference 
in bearing between them the longitude must be correct. If the latitudes do not 
agree the true latitude and longitude may readily be found by plotting on the 
chart, or by the formula used in preceding example, or by No. 2 method explained 
below. 



METHOD No. 2. 

By Aid of Table giving the Error in Latitude by Ex-meridian due to 4 sec. Error 
in Time or i' of Longitude. 

By the aid of the above-named table the double altitude problem may be 
worked from the meridian, on the same principle as two chronometer observations 
are worked from a parallel of latitude. If the azimuth is not over 70 (the limit 
of the table), the problem may be worked from the meridian with either an ex- 
meridian and chronometer observation combined or from two ex-meridians. 

When both observations are on same side of meridian, the difference between the 
two errors in latitude, due to i' of error in the longitude, taken from the table, 
will be the divisor for the two differences of latitude resulting from the two observa- 
tions, and will give the correction for the longitude used. 

When one observation is east and the other west of meridian the error of longitude 
will be found by dividing the differences of latitude resulting from the two observa- 
tions by the sum of the factors taken from the table. The error in latitude will 
then be found by multiplying the error in longitude by the correction taken from 
the table (in preference using the azimuth nearest to the meridian) and applying 
this to the ex-meridian latitude in the direction of the trend of the position-line, 
which is always at right angles to the bearing of object. 

When the altitude is high and near the meridian the azimuth shouldjjbe 
obtained by the time and altitude. This may be done either by Table D or by 
the rule of sines. (See examples on p. 105.) 




95 



EXAMPLE 2 (p. 105). Both Observations on Same Side of Meridian. 




21 ' N., long, by chron. from 
46' 55" W. and position-line 



a 7-5' Log 0-8751 

B 32 Sin 9-7242 

A 40 Cosec 0-1919 



b 6'i8' Log 0-7912 
C 72 Cos 9-4900 



Cor. for lat. C D 1-91^ Log 0-2812 

i' 54'6" 



With lat. 46 

obsn. gave 14 

32 E. . 

With long. 14 46' 55'' W., lat. by ex-mer. from 
second obsn. gave 46 28' 30" N. and position- 
line N. 72 E. 

For the figure. From B, in lat. 46 21' N. and 
14 47' W., draw a meridian-line to C = lat. 46 
28-5' N. ; and from B and C draw two lines N. 32 
E. and N. 72 E. respectively to cut one another at 
A. From A drop a perp. on B C produced at D. 

We now have in the right-angled triangle ABD 
arjgle B 32 .*. A = 58 ; and in the right-angled 
triangle ACD angle C = 72 .'. A = 18 

In the triangle ABC, A will therefore = 40 

Then in the triangle ACB, B = 32, A = 40, 
and a 7-5' 

First find b, then CD = lat. cor., and AD = 
long. cor. 

Formula. 
b = a sin B cosec A 



C D = 6 
A D = b 
b 
A 



cos C 
cos A. 

6'i8' Log 0-7912 
1 8 Cos 9-9782 



Cor. for long. A D 5"88' fl Log 0-7694 
5' 52-8" 



Lat. by ex-mer. 46 28 30 N 
Cor. i 55 N 



Correct lat. 46 30 25 N 



Long, by chron. 14 46 55 W 
Cor. 5 53 E 



Correct long. 14 41 2 W 



BY No. 2 METHOD. 



ist obsn. Q's Az. S 66 E gives (Table M, pp. 150-151) 1-59 N to Ed. 
2nd obsn. O's Az. S 25 E gives (Table M, pp. 150-151) 0-32 N to E<1. 



Diff. 



Lat. error 

1-27' 



Long, 
i' 



Dift. lat. 
7'5' 



1-27 



Long. cor. 



Lat. (i) 46 21 -o N 
Lat. (2) 46 28-5 N 



1-27 ) 7'5 ( 5*9 E x -32 = Lat. cor. r888 N 



Lat. by ex-mer. (and obsn.) 
Cor. 



46 28-5 N 
1-9 N 



Long. 
Cor. 



14 46-9 W 
5'9 E 



46 30-4 N Long. 




Lat.46'21' 



96 



EXAMPLE 3. Two Ex-meridians on Different Sides of the Meridian. 

AT TIME OF 2ND OBSERVATION. 

With long. D.R. 2 35' 40" W., lat. by ex-mer. a.m. Obsn. 10 10-4' S. and 
position-line for plane chart N. 64-8 W. 

With long. D.R. 2 35' 40" W., lat. by ex-mer. p.m. Obsn. 9 55-9' S. and 
position-line for plain chart S. 63-7 W. 

For the figure. From A in lat. 10 10-4' S.'and long. 2 35-7' W. draw a 
meridian line to B at 9 55'9' S. and from A and B draw two lines N. 64-8 W. and 
S- 63-7 W. respectively to cut one another at C. From C drop a perpendicular 
on A B at D. 

In the right-angled triangles A C D and B C D the angles at C will be 
respectively 25-2 and 26-3, and therefore the angle at C in the triangle ABC 
will equal 51-5. We then have in the triangle A B C, A = 64-8, C = 51-5, and 
A B (diff. lat.) = 14-5'. First find a, then B D = lat. cor., and C D = long. cor. 

Formula.. 

a = A B sin A cosec C 
B D = a cos B 
C D = a ' cos B C D 

AB 14-5' Log 1-1614 
A 64 48' Sin 9-9566 
C 51 30' Cosec 0-1066 



1677' Log 
63 42' Cos 



1-2246 
9-6465 



B D d. lat. 7-43 0-871 

Cor. ' "jriS 
Lat. n 10 3-3 S 



BCD 26 1 8' Cos 
C D long. Cor. 15*04' 



1-2246 



1-1771 



Long. 
Cor. 



2 357 W 
15-0 W 



Long, in 2 50-7 W 





B Lai 955-9'S, 

Long235-7'W. BY No. 2 METHOD 



A.M.obsn. O's Az. N 25-5 E gives (Table M, pp. 156-157) -47 N to Wcl. 
P.M.obsn. O'sAz N 267 W gives (Table M, pp. 156-157) -50 S to W<1. 



Lat. error 
'97' 



Long. 

T' 



Sum 



Diff. lat. 



97 : i' long' 



Long. cor. 
15' W. 



Lat. (i) 10 10-4 S 
Lat. (2) 9 55-9 

97 ) 14-5 ( 15 x -5 = 7-5 S 



Lat. (2) 9 55-9 S 
Cor. 7'5 S 



Lat. in 10 3-4 S 



Long. 2 35-7 W 

Long. cor. 15-0 W 

Long, in 2 50-7 W 



Wj% 



97 



REMARKS ON THE POSITION-LINE AND " SUMNER " PROBLEM IN 
CONNECTION WITH EX-MERIDIANS. 

Although most navigators are now fully alive to the value of the position-line 
in connection with the longitude by chronometer, the value of the position-line in con- 
nection with the latitude by ex-meridian is seldom presented in works of navigation. It 
is generally supposed that an ex-meridian, if taken within a certain time from noon, 
will give a correct latitude, and that therefore the ship's line of position is anywhere 
on that parallel of latitude. This, however, is only the case when the ship time (which 
depends on the longitude) is nearly correct. 

The further the object is in bearing away from the meridian the greater will be the 
error due to an error in the time. (See Table M, pp. 156 and 157). 

The time, however, might be uncertain to 4 or 5 minutes, and yet the ex- 
meridian observation may be of great value in connection with the position-line, 
either when near the land by combining this line of bearing with some sounding 
or bearing of the land (see p. 170), or by combining it with another astronomical 
position-line, as in the " Sumner " problem. When the body which is used as an 
ex-meridian is within the limits of ex-meridian tables, an accurate starting point 
for a position-line may be obtained with very few figures. For cases where the 
body is outside the usual ex-meridian limits, a formula is here given (pp. 97 to 98) 
which will give a correct latitude for any time from the meridian corresponding to 
the true hour-angle of the sun or other heavenly body, and the latitude on an 
approximate D.R. longitude will give the starting point for the position-line which 
these tables give, cutting this longitude meridian, at that latitude. 

It is very generally believed by navigators that an observation taken near the 
meridian is of no use in connection with the " Sumner " problem. To some extent this 
is true when the problem is worked by the usually taught methods, and the D.R. 
latitude is much in error. I have endeavoured to show by the following examples how 
the ex-meridian problem may be combined with the chronometer observation in the 
"Sumner" problem: and, if this is done, it matters little how the sun or stars bear 
when the observations are taken, provided there is a suitable difference in bearing (say, 
3 points or more) between the two position-lines. 

The latest ex-meridian tables by Blackburne and Westland enable the navi- 
gator to very readily obtain his position from two ex-meridians, or by an ex- 
meridian and chronometer observation, which may be worked as a double altitude, 
or plotted on the chart, just as accurately and even more rapidly than it could be 
done from two chronometer observations. 

When observations are taken at the best possible time shortly before sunrise and 
after sunset, when probably only three or four of the brightest stars are visible we can 
not expect always to get two stars sufficiently far from the meridian and prime vertical 
as is considered by some necessary (vide " Wrinkles," gth Ed., p. 514) for a satisfactory 
double altitude to be worked on the " Sumner" principle. However, if advantage is 
taken of the methods shown in the following examples, it will be seen how little this 
matters. The only necessary condition of importance to insure good results is that the 
stars should be sufficiently far apart in bearing to give a good cut ; and if one observa- 
tion be near the prime vertical, and the other one near the meridian, the writer would 
say so much the better, rather than that this should be looked upon as an objection. 

The following figures give the cases for any time from the meridian, when from a 
given hour-angle the latitude is required to be found. 



LATITUDE BY EX-MERIDIAN WHEN OUTSIDE ORDINARY LIMITS,)' 

CASE No. i. Object above the Pole, Angle at Z ( = Bearing of Object) more than 
90 reckoned from Observer's Pole. 

In the spherical triangle Z P D, let Z P = 
co-lat, Z D = co-alt, and PD = Polar Dist. 

Given Z D, PD, and angle at P : to find 
P Z = co-lat. 

From D drop a perpendicular on the meri- 
dian at M, then in the right-angled spher. 
triangle P M D we have P D and angle at P 
to find PM = arc (i). 

Formula. -Cos P = tan (i) cot PD .'. 
tan (i) = cos P tan PD. 

Next find Z M = arc (2). 

In the spher. triangle P M D, cos PD = 
cos (i) cos M D. 

In the spher. triangle Z M D, cos Z D = 
cos (2) cos M D. 

Cos (2) Cos ZD _ | COS(2)=COS(I) . 

"Cos (l ) CosPD " I cosZD-secPD. 
PZ (co-lat. = arc (i) - arc (2). 
7 Azimuth. 




98 



CASE No. 2. Angle at Z less than go c 



Same formula as in previous case, but 
P Z (co-lat.) = arc (i) + arc (2). 




CASE No. 3. Object below the Pole. 



In the spher. triangle P M D, angle at P = 
supplement of hour-angle. Then follow the 
same formula as in Case No. i 

P Z (co-lat.) = arc (2) - arc (i). 




By using the complements of PD and Z D, and comp. of P M for arc (i) when 
object is above the Pole, or comp. of Z M when object is below the Pole, the formula 
may be arranged as follows, and the rule as below applied : 

OBJECT ABOVE THE POLE. 

Cot arc (i) = cos H.A. x cot decl. 

Cos arc (2) = cosec decl. x sin arc (i) x sin alt. 

Name arc (i) same as decl. 

Name arc (2) contrary to bearing of object i.e., N. or S. of the prime vertical. 

Add like and subtract unlike names. Sum or diff. of arc (i) and arc (2) = latitude. 

OBJECT BELOW THE POLE. 

Tan arc (i) = cos suppt. of H.A. x cot decl. 

Sin arc (2) = cosec decl. x cos arc (i) x sin alt. 

Name both arc (i) and arc (2) same as the decl. 

Latitude = sum of arc (i) and arc (2) always named same as the decl. 

NOTE.- It is not advisable to use the formulae here given when other methods can 
be used, if the declination of object is within 3 or 4 N. or S. decl. If it is then used, 
six-figure logarithms should be taken out, and the corrections made for odd seconds 
of arc. 

Examples in the use of these formulae are given in the problems following. 




99 

FORMULAE FOR EX-MERIDIANS. 

WORKED-OUT EXAMPLES TO ILLUSTRATE EACH CASE. 

As some have been puzzled in trying to follow the ex-meridian formulas from the 
figures here given when latitude and declination are of contrary names, owing to P D 
and P M being over 90, the reader is reminded that to take out the tan and sec of 
an arc if over 90 he must take out the cotan and cosec of amount in excess of 90. 

If the rule is followed independently of the figure this confusion will be avoided, 
as decl. and alt. are used, instead of P.D. and Z.D. 

Examples of each case, following either figure or rule, are here fully worked out 
which can be easily followed. 

CASE No. i. Hour-angle ah. iym. ios., Lat. S., Decl. 23 N., and Altitude 16 N. 

Required the latitude. 



FORMULA FROM THE FIGURE. 



FORMULA DEDUCED AS PER RULE. 



Co-lat 


H.A. 
PD 

PM 

ZM 
.PZ 
Lat. 


H. M. S. 

2 17 IO 

113 
117 ii*' 

71 ii| 


Cos 9-91707 
Tan 0-37215 


Sec 0-40812 
Cos 9-65989 
Cos 9*44034 


H. M. S. 

H.A. 2 17 10 
Dl. 23 N 

Arc(i)27ui'N 
Arc (2) 71 "*S 


Cos 9-91707 
Cot 0-37215 


Cosec 0-40812 
Sin 9-65989 
Sin 9-44034 


Tan 0-28922 


Cot 0-28922 
Alt. 16 


Cos 9-50835 


Cos 


9-50835 


46 





Lat. 


44 o 


S 


44 


oS 








CASE No. 2. Hour-angle ih. 38m. las., Lat. N., Decl. 40 N., and Altitude 61 N. 

Required the latitude. 

. M. s. 

Cos 9-95885 

Cot 0-07619 Cosec 0-19193 

Cot 0-03504 Sin 9-83126 
Alt. 61 Sin 9-94182 
. Cos 9-96501 



H.A. 
PD 

PM 

ZM 
Co-lat. PZ 
Lat. 


H. M. S. 
I 38 12 
50 

47 i8J' 
2241$ 


Cos 9-95885 
Tan 0-07619 


Sec 0-19193 
Cos 9-83126 
Cos 9-94182 


H. M. S. 

H.A. i 38 12 
Decl. 40 

Arc (i) 42 4ii' N 
Arc (2) 22 41 i S 


Tan 0-03504 


ZD 29 


Cos 9-96501 


70 o 
20 o N 


Lat. 20 o N 


^^^^ 



CASE No. 3. Hour-angle 9 h. 23m. 475., Lat. S., Decl. 62 34' S., and Altitude 22 S. 

Required the latitude. 



H. M. S. 

H.A. 9 23 47 

12 O O 



Supt. 2 36 13 Cos 9-89017 

PD 27 26' Tan 9-71524 Sec 0-05181 

PM 21 57j' Tan 9-60541 Cos 9-96731 
ZD 68 Cos 9-57357 
ZM 66 571 . . . . 
Co-lat. PZ 



Cos 9-59269 




H. M. s. 
H.A. 9 23 47 

12 O O 



Supt. 2 36 13 Cos 9-89017 

Decl. 62 34' S Cot 9-71524 Cosec 0-05181 

Arc (i) 21 57j' S Tan 9-60541 Cos 9-96731 

Alt. 22 Sin 9-57357 



(Comp)Arc(2) 23 2|S 
Lat. 45 o S 



Sin 9*59269 



The accuracy of this method may easily be proved by reversing the process, and 
finding the hour-angle from the latitude, declination, and altitude given. 

Case No. 3 is especially useful, as with high-declination stars the latitude will 
generally be fairly correct, even when the time is in error a couple of minutes and the 
body observed is an hour or more from the meridian below the Pole. For instance, in 
the latitudes of last example, an ex-meridian of # a Crucis with hour-angle n h., or i h. 
from meridian below the Pole, and 2m. of error in the time used, would only cause an 
error of 2^' in the resulting latitude. 



100 

DOUBLE - ALTITUDE POSITION BY TWO SUN OBSERVATIONS. 

1902. March agth, p.m., the following observations were taken in the artificial horizon, at 56 Hawker Street, 
Wellington : 

D. H. M. s. = o / ,/ 

M. T. G. by chron. 28 13 17 31 Obsd. alt. of O 89 o 30 

28 15 51 18 52 5 10 

Required the true bearing of the sun at each observation, and the position of place, assuming latitude to be 41 o' S. 
Index error of sextant + i' 23"; ther. 70; bar. 30'oin. 



IST OBSERVATION. 



2ND OBSERVATION. 



M.T.G. 


D. H. M. S. H. 

28 13 17 31 Dl. var. 58*52 x 10*71 


D. H. M. S. 

M.T.G. 28 15 51 18 


H H - 
Dl. var. 58*51 x 8*15 


N 

N 


Before noon, 2gth 10 42 29 , 


Before noon 


8 8 42 =8*ishr. 


, 


Eq. T. var. 

Cor. 
Eq. T., 2gth 

Cor. Eq. T. 

Obsd. alt. O 
I.E. 

App. alt. 
Ret. and par. 

Semi-d. 

T. alt. 
Lat. 
P.D. 

S 
S-A 

H.A. 
Eq.T. 


s. H. Dl., 2gth 3 7 20-7 N 


S. H. 

Eq. T. var. 0-767 x 8'i 


Dl., 2gth 3 7 20-7 


Cor Dl 2 r 6 r 4 N 


Cor. Dl. 2 59 24 
P. D. 92 59 24 


+ 8'2 P.D. 92 56 54 


Cor. 
Eq. T., 2gth 

Cor. Eq. T. 

Obsd. alt. O 
I.E. 

App. alt. 
Ref. and par. 

Semi-d. 

T. alt. 
Lat. 
P.D. 

S 
S-A 

H.A. 
Eq.T. 

M. T. place 
M. T. G. 

Long, in T. 

Long. (2) 
Long, (i) 
rt 
Diff. long. 

N to E (i) to A 
N to E (2) to A 

: d. long. 54*7 : : lat. 

used 41 o o S 
18 30 S 


M. S. 

+ 6-2 
5 5'i 


5 5 J- 


Sec 0-122220 
Cosec 0*000591 

Cos g-245045 
Sin 9'go85g4 


5 13-3 + A. T. 


5 "*3 


89 o 30 
+ i 23 


52 5 io 
+ i 23 


2 ) 89 i 53 


2 ) 52 6 33 


44 30 56*5 
50*5 


26 3 16*5 
- i 44 


44 30 6 
- 16 2 

44 14 4 
41 o o Sec 0-122220 
92 56 54 Cosec 0*000575 


26 i 32*5 
16 2*5 


25 45 30 
41 o o 
92 59 24 


178 10 58 


159 44 54 


89 5 29 Cos 8-200237 
44 51 25 Sin 9*848398 


7g 52 27 
54 6 57 


oh 55m 58-63 Sin2 8*171430 
+ 5 13-3 === 


3h 26m 8'8s 
+ 5 "'3 


Sin2 g-27645o 

A -69 N 
B -07 N 


M. T. place 2( 
M.T.G. 2f 


j i i 11*9 A 3-49 N 
J 13 17 31*0 B -22 N 


2g 3 31 20-1 
28 15 51 18*0 


Long, in T. 


ii 43 40-9 Cor. 3-71 N 


II 40 2-1 


Cor. -76 N 


Long, (i) 


175 55' 13" E C gives Az. N 19-7 W 


175 o 31 E 
175 55 13 E 


C gives Az.N 60-2 W 


A. 

I'O 


T. C2 gives Pos.-line for plane cha 

N 7 5E 


Pos.-line T. C2 N 37-2 E 


54 42 = 54 


Long, (i) cor. = 3*71 
Long. (2) -76 

D. long. 2-95 
(2) 2-95 (i) 


- in Fig. 
i : lat. cor. 18*5 

Long. (2) 
18*5' x -76' = 

Long, in 


175 o 31 E 
14 4 W 




/ /^-"'tor tO S Lat 


in 41 18 30 S 


174 46 27 E 



In this example, with the latitude used in the calculation 17^' in error, the resulting latitude is i' in error. This is due 
to the sun's azimuth differing nearly 2 at the position corresponding to the hour-angle found with 41 lat. from that of ths 
true hour-angle and latitude. If the position had been worked in the usual way as given in the Board of Trade 
examinations with two latitudes, say, 17' in error on each side of the true latitude, the resulting latitude would have been 
just 2' north of that here found, or i' north of the true latitude. When the hour-angle is small, and the two latitudes used 
on each side of the true latitude are far apart, the resulting position line always places the ship on the Equatorial side of the 
true position-line or circle of altitude. When the problem is worked with the D.R. latitude, and a position-line at right 
angles to the bearing of the object observed, the resulting position-line will place the ship on the Polar side of the true line 
of position ; an error of 30' in the D.R. latitude in either case will sometimes make 2' to 3' error in the latitude. When one 
of the hour-angles is not far from the meridian, as in this case, the problem as worked on the following page will give a 
more accurate position, and the work is not longer. 

These observations when reworked on the same principle, when using a latitude near the the truth, give the latitude 
of position within o'i' of the truth. Several observations were taken at the same time, and all the resulting latitudes 
agreed within a few seconds of one another. 

For position of place plotted on the chart, see chartlet on next page. 



101 , ;:>'- /'. '-: UK?''- : /^ 

DOUBLE -ALTITUDE POSITION BY TWO SUN OBSERVATIONS 

(COMBINING CHRON. LONG. OBSERVATION WITH AN EX-MERIDIAN). 

1902. March 2gth, p.m. In assumed latitude 41 o' S. the true altitude of sun's 
centre was 44 14' 4" when a chronometer showed M. T. G. 28 d. 13 h. 17 m. 31 s. ; and 
again on the same afternoon the true altitude of sun's centre was found to be 25 45' 30" 
when a chronometer showed M. T. G. 28 d. 15 h. 51 m. 18 s. Required the position of 
place by projection on the chart. 



IST OBSN. WEST OF MERIDIAN. 



2ND OBSN. WEST OF MERIDIAN. 



M.T. Greenwich 
Long, in T. by 2nd obsn. 

M.T. place 
Bq.f. 



O's H.A. 
O's Dl. 
Arc (i) 



Arc (2) 
Latitude 



3 i 36 N 

44 15 56 S 
41 14' 20" S 



D. H. M. S. 

28 13 17 31 

+ II 40 2 E 

29 o 57 33 

5 13 

o 52 20 Cos 9-988578 

256'54"N Cotn-288i63 Cosec 11-288738 

. Cot 11*276741 Sin 8*722640 

True alt. 44 14' 4" Sin 9-843604 

Cos 9-854982 



T. alt. 

Lat. 

P.D. 



S 
S-A 



Sec 
Cosec 
Cos 
Sin 

Sin2 



25 45 30 
41 o o sec 
92 59 24 cosec 



159 44 54 



79 52 27 cos 
54 6 57 sin 



0*122220 
0-000591 
9-245045 
9-908594 

9-276450 



H. M. S. 

H.A.=A.T.place3 26 8*8 
Eq. T. + 5 11-3 



oh. 52m. 
Lat. 4 ii S 
Dl. 3 N 

Pos.-line from Table C2 N 76 E 



3-80 N 
23 N 



M. T. place 
M. T. G. 

Long, in T. 
Longitude 



9 3 3i 20-1 
3 15 51 18 

ii 40 2-1 
i75o' 3 i"E 



POSITION BY CHART. 

Lat. 4i i7j S 
Long. 174 47 E 



H.A. sh. 26m. 

Lat. 41 S A -69 N 

Dl. 3N B -07 N 

Pos.-line from Table C2 N 37-2 E -76 N 



I7430'E 40' SO' I75 e 0' to- 



JO' 40' SO' 176 O' 



JO 





to- 



20' 



30' 



Position by two chron. observations 
(see previous page) 



Lat 4i i8 S. 
Long. 174 4 6| E. 



At^>>V -102 

The following example is taken from Captain Thompson's excellent book, 
" Navigation Simplified," which, I presume, is now in the hands of nearly all those 
navigators who desire to obtain the highest certificates. This example is taken as the 
work is there given in detail, with the plotting on the chart, so that the reader can 
compare the working, and see for himself the saving in figures, while maintaining equal, 
if not greater, accuracy by using the A and B Tables. 



POSITION BY DOUBLE ALTITUDE OF SUN. 

1900. July and, at about 6h. 50 m. a.m., and again at n a.m., from the following 
observations : 



Mean Time at Greenwich by Chron. 
D. H. M. s. 
i 7 43 12 
i ii 57 36 



True Altitude of the Sun's Centre. 

O I II 

25 5i 6 
69 50 25 



Find the true bearing of the sun when the first altitude was observed, and the 
position of the ship when the second altitude was taken, assuming the ship to be 
between latitudes 49 50' N. and 50 20' N. The ship's course and distance between the 
observations was N. 67 W., dist. 30 miles. 



O , ,i M. S. oil, M. S. 

istobsn. O'sCor.Dl.= 23 6 49 N Cor.Eq.T. 3 35 + A. T. 2ndobsn.O'sCor.Dl.= 23 6 7N Cor.Eq.T. 3 36-4 
90 o o 90 o o 



N. P. D. 



66 53 ii 



N.P.D. 



66 53 53 



Run between observations, N 67 W 3om. = 117' N 
IST OBSN. 

A 25 51 6 
49 50 o Sec 0-190431 
P 66 53 ii Cosec 0-036340 


27'6' W = 

L 
P 

S 

S-A 


-43 

2ND 
O 

60 
50 

66 


' d. long. 
OBSN. 

i 42 
53 53 


Lat. (i) 49 
Run. d. lat. 


50 o N 
ii 42 N 


Lat. (2) 50 


i 42 N 


Sec 0-192188 
Cosec 0-036302 

Cos 8-289773 
Sin 9-672223 




S 

S-A 


142 


34 


17 


Cos 
Sin 

Sin2 

A 
B 

C 


9-506301 


177 


46 





45 


17 

26 


8-5 
2'5 


88 
28 


53 
2 


o 
35 


H. 

24 

H. A. east - 5 


M. 
O 

6 


s. 



58 


H. 

24 

H.A. - o 


M. 


57 


s. 



13-5 


9-585822 

28 S 
44 N 

16 N gives Az.N 84 E 


Sin2 8-190486 

A 4-68 S 
B 1-72 N 

T.C 2-96 S Posn.-line for 
^-^. plane chart, 

See 7 Ta\>leC2 

2-96 S to W and N to E 
i6NtoW 

3-12 sum of A and B cor. 


A. T. ship 
Eq.T. 

M. T. S. 
M.T.G. 

Long, in T. 

Long. 
Run d. long 


18 

+ 


53 
3 


2 

35 


A. T. ship 
Eq.T. 

M.T.S. 
M.T.G. 

Long, in T. 

Long. (2) 
Long, (i) 

D. long. 


23 


2 

3 


46-5 
36-5 


18 
7 


56 

43 


37 
12 


23 
ii 


6 
57 


11 


ii 


13 


25 


Pos.-line for plane chart, 
Table C2, gives N 9- iW 


ii 


8 


47 


168 


21 

43 


15 E 
oW 


x67 

167 


i 

ii 

38 


45 E 
15 E 


Long, (i) 167 
Cor-i6'x8'5' 


38 

I 


15 E 

22 W 




26' 


30" 











Long, in 167 36 53 E at time of and observation. 



d. long. d. long. 
3-12' : 26-5' : 



lat. 
i' 



lat. 
8-5' cor. 



Lat. at 2nd obsn. 50 i 42 N 
Cor. 8 30 N 



Lat. in 



50 10 12 N 



Cor to N 



For position of ship when plotted on the chart, see chartlet on next page. 



103 



DOUBLE ALTITUDE OF THE SUN 

(COMBINING CHRON. LONG. OBSERVATION WITH AN EX-MERIDIAN). 
igoo. and July, at about 6h. som. a.m., and again at n a.m., from the following 
observations : 

Mean Time at Greenwich by Chron. True Altitude of the Sun's Centre. 

D. H. M. s. / u 

i 7 43 12 25 51 6 

i u 57 36 60 50 25 

Find the true bearing of the sun when first altitude was observed, and the position 
of the ship when the second altitude was taken, assuming the ship to be between 
latitudes 49 50' N. and 50 20' N. The ship's course and distance between the 
observations was N. 67 W., dist. 30 miles. 



ist obsn. O's Cor. Dl. = 23 6 49 N 
90 o o 



N. P. D. 



66 53 ii 



2nd obsn. O's Cor. Dl. = 23 6 7N 
90 o o 



Cor. Eq. T.= 3 35 + A.T. 



M. S. 

Cor. Eq. T. = 3 36-4 + A.T 



N. P. D. 66 53 53 

Run between observations, N 67 W 30 m. = 27-6 m. dep. = 43' W d. long. 



IST OBSN. 



2ND OBSN. 
H. M. s. 



A 25 
L 49 
P 66 


5i 
50 
53 


6 
o Sec o' 190431 
ii Cosec 0-036340 


M.T. ship23 8 9 (see M.T. ship, ist ob: 
Eq. T. - 3 36 


A.T. ship 23 4 33 

24 o o 


142 


34 


17 


S 71 
S-A 45 


17 
26 


8*5 Cos 9-506301 
2'5 Sine 9-852750 


H.A. o 55 27 Cos 
Dl. 23 6' 7" Cot 


9-987163 
0-370003 


H. 

24 

H.A. east - 5 


M. 



6 


s. 


Arc (i) 23 
Arc (2) 26 


43' 10" N Cot 
T. alt. 

27 22 N 


0-357166 


58 Sin2 9-585822 


60 50' 25" 

478 S 

175 N 


A. T. ship 18 
Eq. T. + 


53 
3 


2 

35 


Lat. 50 


10' 32" N 


M. T. ship 18 
M. T. G. 7 


56 

43 


37 

12 


H.A. oh 5601 E 1 
Lat. 50 N \ A 
Dl. 23 N j B 


Long. inT. 11 


13 


25 


Longitude 168 
Run d. long 


21' 

43 


15" E 

oW 


Long. (2) 167 38 


15 E = ii 10 33 



Cosec 0-406306 
Sin 9-604505 
Sin 9-941146 
Cos 9-951957 



M.T. G. + ii 57 36 
M.T. ship 23 8 9 



H.A. 5h. 8m E 
Lat. 50 N 

Dl. 23 N 



A -28 S 

B -55 N 



Cor. T. C. 3-03 S gives Az. S27'4E = 
= Pos.-line for 

plane chart, 
Table ca, S 
71-7 W and 
N 71-7 E 



Cor. Table C V[6 N gives Az. N 84-1 E and Pos.-line for plane chart, Table C2, N 9 W 

Chartlet for Problem on page 102. For above Problem. 



tc 




I67"30 L 



104 

With the desire to show tfce especial utility of these tables for obtaining accuracy 
of position and conciseness in work, and the superiority of the method here advocated 
over the method still employed in the Board of Trade Examinations of Masters and 
Mates, for the " Sumner " problem, the following example is given and plotted on the 
chart by both methods. For the sake of better illustrating the possible error due to the 
old method, a wider range of latitude has been taken than is usually given in the 
examination papers, though, considering the high speed of some of the present-day 
steamers, the range is not excessive, as the run in interval itself might often amount 
to over i of latitude 



"SUMNER" PROBLEM AS GIVEN IN THE B. OF T. EXAMINATIONS. 

1898. On aoth June, a.m., at ship, at sea, and uncertain of my ship's posi- 
tion: when a chronometer indicated M. T Green. 19 d. 22 h. 30 m. the true altitude 
of sun's centre was 52 9'; and again, a.m. on same day, when chronometer indicated 
20 d. oh. i6m. the true altitude of sun's centre was 65 18', the ship having made 
23 miles on a true N. 24 E. course during the interval between the observations. 
Required the line of position and true bearing of the sun at time of is-t observation ; and 
the position of the ship when 2nd observation was taken assuming latitudes 46 N. 
and 47 N. 



ist obsn, 



M. T. Green. 
Eq. of time 



D. H. M. s. 
19 22 30 o 
i 167 



A. T. Green. 19 22 28 43-3 



D. H. M. s. 

2nd obsn. 20 o 16 o 
i 177 



A.T. G. 20 o 14 42-3 P. D. 66 33 





A 
L 
P 




52 9 

46 o 
6633 




S 

s- 


164 42 


82 21 

-A 30 12 


H.A, 

A.T. 
A.T, 




0. H. M. S. 

2 31 18-8 E 


shipig 21 28 41-2 
G. 19 22 28 43*3 



IST OBSERVATION. 



Sec 0-158229 
Cosec 0-037438 



Cos 
Sin 



9-124248 
9701585 



Long, in T. i o 2'i 
Long. A 15 o' 31" W 



Sin2 9-021500 



S 
S-A 



52 9 
47 o 
6633 

165 42 

82 51 
30 42 



Sec 
Cosec 



Cos 
Sin 



0-166217 
0-037438 



9-095056 
9-708032 



H.A. 



D. H. M. S. 

2 28 40-3 E 



Sin2 9-006743 



A.T. ship 19 21 31 19-7 
A.T.G. 19 22 28 43-3 



Long, in T. o 57 23*6 
Long. B 14 20' 54" W 



65 18 
46 o 
6633 

177 5i 



t 88 55i 
- A 23 37! 



D. H. M. S, 

o 49 53-1 E 



H.A. 

A.T. ship 19 23 10 6-9 
A.T G. 19 24 14 42-3 

Long, in T. 14 35-4 
Long. C 16 8' 51" W 



2ND OBSERVATION. 



Sec 0-158229 
Cosec 0-037438 



Cos 
Sin 



8-273260 
'9*602872 



65 18 



178 51 



8925* 

-A 24 7t 



Sec 0-166217 
Cosec 0-037438 



Cos 
Sin 



8-001538 
9-611435 



H.A. 



D. H. M. S. 

o 37 9'2 E 



Sin2 7-816628 



A.T. ship 19 23 22 50-8 
A.T.G. 1924 14 42-3 



Long, in T. o 51 51-5 
Long. D 12 57' 52" W 



Line of position N 24* E Position at 2nd obsn. Lat. 46 27' N 
Sun's bearing S 654 E Long. 14 43* W 



Trueposn. Lat. 46 30' 20" N 
Long. 1 4 41' o"W 



105 

SUMNER PROBLEM FACILITATED BY A, B, AND C 2 TABLES. 

1898. On 2oth June, a.m., at ship, at sea, and uncertain of my ship's position : when a chrono- 
meter indicated M. T. Green. 19 d. 22 h. 30 m. the true altitude of sun's centre was 52 9' ; and again 
on same day when chronometer indicated 20 d. o h. 16 m. the true altitude of sun's centre was 
65 1 8', the ship having made 23 miles on a true N. 24 E. course during the interval between the 
observations. Required the line of position and true bearing of the sun at time of ist observation ; 
and the position of the ship when and observation was taken, assuming D.R. latitude to be 46 N. 
when ist observation was taken. 



IST OBSN. 

D. H. M. S. 

M.T. Green. 19 22 30 o 
Eq. of time i 167 

A. T. Green 19 22 28 43-3 

Decl. 23 27' N - P. D. 66 33' 



2ND OBSN. 

D. H. M. S. 

M.T.G. 20 o 16 o 
Eq. of time i 17-7 



A.T. Green. o 14 42*3 
Long, (i) - o 59 77 W 

A.T. ship 



Run N 24 E 23 = 21 N 9*4 E = 13-6 d. long. 
Lat. (i) 46 o N 



Lat. D.R. 



46 21 N at time of 2nd obsn. 



52 9 
46 o 
6633 

164 42 



Sec 0-15825 
Cosec 0-03743 



H.A. 



o 44 25-4 



S 82 21 

S - A 30 12 

D. H. M. S. 

H.A. 2 31 18-8 


Cos 9*124248 
Sin 9701585 


A 1-33 S 
B 0-71 N 


Sin2 9-021500 

H.A. 2h. 3 2m.\ 
Lat. 46 N 1 

Dl. 2 3 N j 
C 2 gives Posn 


A.T. ship 1921 28 41-2 
A.T.G. 19 22 28 43-3 


Long, in T. i o 2-1 

Long. i5o'3i"W 
Run. d. long. 13 36 E 


C 0-62 S gives Az. S 667 E. 


.-line for plane chart N 31*8 E 



Long, (i) 14 46 55 W 
Long, in T. oh sgm 7-73 



Lat. 46 21' N and Posn.-line N 32 E 

o i 

Position from chart. Lat. 46 30*5 N 
Long. 14 41 - o W 



FOR Az. BY TABLE D. 

M. o 

Az. (H.A.) 44-4 = in ) (p. 81) 

Lat. (decl.) 23-5 N [ M = 22'6 

Lat. (alt.) 65-3 I (p. 82) 

M. 22-6 $ gives Az. 25, which gives 

(p. 49) A & B 3-10'. 

A & B 3-10' gives (p. 75) posn.-line for 
Plane Chart N. 72 E. 



LAT. BY EX-MER. TABLE No. 3. 



Decl. 23 27' N 
H.A. 



Arc (i) 



Az. 

Alt. 



25 o 
65 18 S 



Z D 24 42 N 



Arc. cor. + 23*8 
Dec. 23 27-0 N 



23 50-8 N 



Arc cor. 2 4*2 
ZD 24 42-0 N 



Arc (2) 22 37-8 N 
(1) 23 50-8 N 



Lat. 



46 28-6 N 



RULE FOR FINDING LATITUDE BY EX- 
MERIDIAN TABLE No. 3 (ABOVE POLE 
OBSERVATION). 

With declination at side and hour-angle from top 
take out arc reduction. 

Add this reduction to the declination for arc (i). 
Name it the same as declination. 

With altitude at the side and azimuth from the top 
take out 2nd arc reduction. 

Subtract the reduction from Z D for arc (2) . 
Name arc (2) contrary to bearing of object. 

Latitude = arc (i) arc (2). 
+ when arcs are of like names. 
- when arcs are of unlike names. 




NOTE. This problem worked by the old method (which is still used in the Board of Trade 
examinations) would give a result 3^' in error in the latitude and 2' in error in the longitude. (See 
page 104.) 



106 

EXAMPLE TO SHOW METHOD OF FINDING THE TRUE LINE OF 
POSITION OR CIRCLE OF ALTITUDE BY USE OF THE A AND B 
TABLES. 

This is given in response to an inquiry by a correspondent, who asked for an 
explanation of author's remark about the tables doing this, in the preface to the first 
edition in 1883. 

EXAMPLE PLOTTED ON CHARTLET FACING PAGE 104. 



Lat. 46 o N \ A 477 S 
IM. 23 27 N I B 2-05 N 

H.A. 049EJC 272StoWorNtoE 

/ M. S. 

Cor. for 10' N = 27*2 E = i 49 



C , o H. M. S, 

Lat. 46 o gives Long. 16 8-9 W H.A. o 49 53 
Cor. for 10 N = 27-2 E - i 49 



Lat. 46 10 N gives Long. 15 417 W 



o 48 4 
-10 

o 47 o for next. 



Lat. 46 15 N\ A 5-02 S 
Dl. 23 27 N I B 2-12 N 

H. M. 

H.A. o 47 Ej C 2-908 

, M.S. 

Cor. for 10' N = 29-0 E = i 56 



a , o i H. M. s. 

Lat. 46 10 N gives Long. 15 417 W H.A. o 48 4 
Cor for 10 N = 29*0 E i 56 



Lat. 46 20 N gives Long. 15 127 W 



o 46 8 
- i o 



o 45 o for next. 



Lat. 46 25 N \ A 3*28 S 
Dl. 23 27 N I B 2-22 N 

H. M. I 

H.A. o 45 E J C 3-06 S 

, M. S. 

Cor. for 10' N = 30-6 E = 2 a 



01 o i H. M. S. 

Lat. 46 20 N gives Long. 15 127 W H.A. o 46 8 
Cor. for 10 N = 30*6 E 2 2 



Lat. 46 30 N gives Long. 14 42'! W 



o 44 6 
-10 



o 43 o for next. 



Lat. 40 35 N \ A 5-56 S 

Dl. 23 27 N I B 2-32 N 

H.M. 

H.A. o 43 EJ C 3-248 

i M. s. 

Cor. for 10' N = 32-4 E = 2 10 



Q| ' H, M. Si 

Lat. 46 30 N gives Long. 14 42'! W H.A. o 44 6 
Cor. for 10 N = 32*4 E 2 10 



Lat. 46 40 N gives Long. 14 97 W 



o 41 56 
i 6 

o 40 50 for next. 



Lat. 4645 N\ A 5'88 S 
Dl. 23 27 N I B 2-44 N 

H.M. 
H.A. o 41 ) C 3-448 

/ M. s. 

Cor. for 10' N = 34-4 E - a 18 



01 o / H. M. S. 

Lat. 46 40 N gives Long. 14 9-7 W H.A. o 41 56 
Cor. for 10 N - 34-4 E - 2 i 



Lat. 46 50 N gives Long. 13 35-3 W 



o 39 38 
i 10 

o 38 28 for next. 



Lat. 46 55 N \ A 6-30 S 

Dl. 23 2 N [B 2-54 N 

H.M. 

H.A. o 3 8i ) C 376 S 



Lat. 
Cor. for 



46 50 N gives Long. 13 35-3 W 
37'6 E 



10 N = 



Lat. 47 o N gives Long. 13 57-7 W 



Cor. for 10' N 



, M. S. 

37-6 E = 2 30 



[NOTE. It will be seen that as the latitude increases so the H.A. will decrease, according to the 
change of longitude, 15' of long, making im change of time in the H.A. Therefore, to get the true cor. 
we must use the mean H.A. and the mean lat. corresponding to the two parallels which we require the 
cor. for. The long, found by the application of the A and B cor. at 47 N is practically the same as that 
found by direct calculation.] 



107 

DOUBLE-ALTITUDE POSITION BY TWO STELLAR OBSERVATIONS. 

1902. On i5th March, p.m., the following observations were taken in the 
artificial horizon, at 56 Hawker Street, Wellington : True position from chart, lat. 
41 17' 32" S., long. 174 46' 57" E. : 

D. H. M. S. , u 

M.T. at Greenwich by chron. 14 21 6 6 Obsd. alt. of * Sirius 11633 otoN.Wd. 
14 22 26 7 * Canopusii2 10 lotoS.Wd. 

Required the true bearing of both stars, and the position of place, assuming 
latitude to be 41 o' S. (17^' in error). Index error of sextant + i' 20". 



D. H. M. S. H. M. S. 

M.T.G. 14 21 66 Sid. T. (G. noon) 23 24 40*46 

M. Q's R.A. + 23 28 8*45 Accl. 21 h. 6m. + 3 27*99 

Sid. T. G. 20 34 14-45 M. Q's R.A. 23 28 8'45 Sid. T. G. 21 54 28*6 M. Q's R.A. 23 28 21-59 



H. M. s. 

M.T.G. 22 26 7 

M. Q's R.A. 23 28 21-6 



H. M. S. 

Sid. T. (G. noon) 23 24 40-46 
Accl. + 3 41-13 



SIRIUS TO N.Wo. 



Obsd. alt. of # 116 33 o 



alt. 



I.E. 



Re? 

A 
L 
P 



S 
S-A 



*'s H.A. 
*'sR.A. 



Sid. T. place 8 14 51-8 
Green. 20 34 14*45 

Long, in time n 40 37-35 



2 ) 116 34 20 

58 17 10 
- 34 

58 16 36 
41 o o 
73 24 46 

172 41 22 




Long, (i) 
17-6' x 1-25' 

Long, in 



175 9' 20" E 
22 o W 

174 47 20 E 



Dl. 16 35 14 S 
90 o o 

P. D. 73 24 46 



Sec 0*122220 
Cosec 0*018460 



Cos 8-804503 
Sine 9*672578 



Sine2 8-617761 



2-00 N 
75 S 



C 1-25 N to 
gives Az. N 46-6 W 
and C' 2 gives Pos.-line 

N 5 i-3 E 
S 51-3 W 



X CANOPUS TO 

1 'I 

Obsd. alt. of * 112 10 10 
I. E + . i 20 


S.Wo. 

O 1 II 

Dl. 52 38 59 S 
90 o o 


2)112 ii 30 

Ap E .ai, -y~s 


P. D. 37 21 i 


Sec 0*122220 

Cosec 0-217036 

Cos 9*587969 
Sin 9*285798 


A 
L 

P 

C 

S-A 

*'s H.A 
*'s R.A. 

Sid. T. place . 
Sid. T. Green 

Long, in time 


56 5 7 
41 o o 
37 21 i 


134 26 8 


67 13 4 
ii 7 57 

H. M. S. 

3 10 41*3 
6 21 47*6 

9 32 28*9 
21 54 28*6, 


W Sin2 9-213023 

A 0-79 N 
B 1*77 S 


C 0*98 S to E 


ii 38 0*3 


gives Az. S 53j W 



Long, (i) 175 9 20 and C2 gives Pos.-line 

S 44'4 E 
Diff. long. 39' 15" 



(2) 



Long, (i) cor. = 1-25 S to W 
(2) 0*98 S to E 

D. long. 2*23 : d. long. 39*25' : : lat. i 1 : lat. cor. 17*6' 



(I) 




Cor to S 



Lat. used 41 o o S 
Cor. 17 36 S 

Lat. in 41 17 36 S 



Long, by Canopus 174 30 5 E 
17-6' x 0*98' = 17 15 E 



Long, in 



174 47 20 E 



The above were bona fide observations taken on a windy night, needing patience to 
wait till the quicksilver was quite steady ; being on different sides of the prime vertical, 
the observations naturally give a good latitude, as i' error of altitude due to instrument 
or refraction would make practically no difference in the resulting latitude. This 
problem reworked with a latitude near the truth only makes a few seconds difference in 
the resulting position. 



[NOTE. A, true alt. ; L, lat. ; P, Polar dist. ; S, half sum ofA + L + P; S-A, diff. between S 
aad A; H. A., hour-angle.] 



108 
DOUBLE-ALTITUDE POSITION BY TWO STELLAR OBSERVATIONS. 

1902. On i5th March, p.m., the following observations were taken in the artificial 
horizon : 

D. H. M. S. Q , u 

M.T. at Greenwich by chron. 14 21 23 43 Obsd.alt. of # a Centauri 69 36 50 to S.Ed. 
H 14 22 26 7 # Canopus 112 10 10 to S.Wd. 

Required the true bearing of both stars, and the position of place, assuming latitude 
to be 41 o' S. Index error of sextant + i f 20". 



IST OBSERVATION. 



H. M. S. 

M. T. Green. 21 23 43 
Sid. T. (G. noon) 23 24 40*46 
Accl. + 3 30-89 



Sid. T. Green. 20 51 54-35 P. D. 29 34 23 



Dl. of X a Centauri. 

60 25 37 S 
90 o o 



2ND OBSERVATION. 



H. M. s. 

M. T. G. 22 26 7 

Sid. T. (G. noon) 23 24 40-46 
Accl. + 3 41-13 



Dl. of * Canopus 

52 38 59 S 
90 o o 



Sid. T. Green. 21 54 28-59 p - D - 37 21 



a CENTAURI TO S.Eo. 



CANOPUS TO S.Wo. 



Obsd. alt. of X 69 36 50 

I.E. +1 20 


Obsd. alt. of # 112 10 10 

I.E. +1 20 


2 ) 69 38 10 


2)112 ii 30 


Sec 0*122220 

Cosec 0*217036 

Cos 9-587969 
Sin 9-285798 


App. alt. 
Ref. 

T. alt. 
Lat. 
P. D. 

S 
S-A 

*'sH.A. 
*'sR.A. 

Sid. T. place 
Sid.T. G. 

Long, in T. 

Long, (i) 
Long. (2) 


34 49 5 
I 22 


Sec Q'12222 

Cosec 0-306684 

Cos 9-782622 
Sin 9-487382 


T. alt. 
Lat. 
P. D. 

S 

S-A 

K'sH.A. 
*'sR.A. 

Sid.T. lace 
Sid. T. G. 

Long, in T. 
Long. (2) 


56 5 45 
- 38 


34 47 43 
41 o o 
29 34 23 


56 5 7 
41 o o 
37 21 i 


IO5 22 6 


134 26 8 


52 41 3 
17 53 20 


67 13 4 
ii 7 57 


rt. M. s. 

5 59 58-0 E Sin2 9-698908 

14 33 i'3 == 


H. M. S. 

3 10 41-3 W 
6 21 47-6 


Sin2 

A 

B 

C 


9*213023 


79 N 
177 S 


8 33 3'3 
20 51 54'3 


A -oo 
B 1-76 S 


9 32 28-9 
2i 54 28-6 

ii 38 0-3 


ii 41 9-0 


C 

E 
E 


1-76 S gives Az.S 37 E 


98 S to E 


175 17' 15" 
174 30 5 


C2 Pos.-line S 60-4 W 


174 30' 5" E 


gives Az.S 534 W 


C2 Pos.-line S 44-4 E. 


^ 






47 10 = 47-17 



Long, (i) cor. = 1-76 S to W 
. (2) 0-98 S to E 

D. long. 2-74 : d. long. 47'iT* : lat. i' : lat. cor. 17-23' = 17' 13" 



Lat. used 41 o o S 
Cor. 17 13 S 



Lat. in 41 17 13 S 



Long. (2) 
17*22' x -98' 

Long, in 



174 30 5 E 
cor. 16 53 E 

174 46 58 E 



(2)2-74 (I) 



These observations were taken on the same evening as those given on the preceding 
page. As one star was east of the meridian and the other one west, the case is not good 
for latitude; but it should give the truest longitude, as instrumental errors, &c., will 
practically eliminate one another in the resulting longitude. This problem reworked 
with a latitude near the truth makes no appreciable difference in the resulting position. 

For position of ship when plotted on chart, see chartlet on next page. 




109 

DOUBLE ALTITUDE OF TWO STARS 

(COMBINING CHRON. LONG. OBSERVATION WITH AN EX-MERIDIAN). 
1902. On 1 5th March, p.m., the following observations were taken : 

D. H. M. s. o , 

M. T. G.by chron. 14 21 23 43 T. alt. of * a Centauri 34 47 43 to S.Ed. 
M. T. G. 14 22 26 7 * Canopus 56 5 7 to S.Wd. 

Required position of place by projection on the chart, assuming the approximate latitude to 
be 41 o' S. 



CANOPUS TO S.Wo. 



M. H. S. 

M.T.G. 2226 7 

Sid. T. (G. noon) 23 24 40-46 
Accl. + 3 4i'i3 

Sid. T. Green. 21 54 28-59 



Dl. of * 52 38 59 S 
P. D. 37 21 i 



a. CENTAURI TO S.Eo. 



H. M. s. 

M.T.G. 21 23 43 
Long, in T. + ii 38 0-3 



M. T. place 
M. Q's R.A. 



9 i 43-3 
23 28 11-3 



H. M. s. 

Sid. T. G. noon 23 24 40-46 
Accl. + 3 30-89 



M. Q's R.A. 23 28 11-35 



A 
L 
P 


56 5 7 
41 o o 
37 21 i 


Sec O- 122220 

Cosec 0-217036 


*'sR.A. 
*'sH.A. 
Supt. 
Dl. 
Arc (i)* 

Arc (2) 
Latitude 


14 33 


rj 


Cos 
Cot 

Tan 


*'sDl. 

8-132720 
9-753933 


= 60 25 37 S 


6 3 


6-7 


Cosec 0-060617 
Cos 9-999987 
Sin 9-756366 
Sin 9-816970 


134 26 8 


5 56 
89 13' 
60 25 

26' 

41 o 


53-3 i 
20" ] 
37 

29" S 
ii S 


S 


67 13 4 
ii 7 57 


Cos 9-587969 
Sin 9-285798 


*'sH.A. 
K'sR.A. 

Sid. T. place 
Sid. T. G. 

Long, in T. 
Long. 


7-886653 


H. 

9 
21 


M. S. 

10 41-3 W 

21 47-6 


Sin2 

A 
B 

Cor 


9-213023 

79 N 
i-77 S 


Alt. 34 47' 43" 

oi S 
i-77 S 


32 28-9 

54 28-6 


41 26 


40 S 








A 
B 


II 38 0-3 


98 S Pos.-line from C2gives S 44-4 E 


174 


30' 5" E 


Cor i -78 


S gives Pos.-line S 60-7 W 



The chartlet below serves to illustrate both the problem above and the one on previous page. 
In the first case the position-lines are laid down from the two longitudes corresponding to the 
parallel of latitude 41 S., and in the second case the position-lines are laid down from the meridian 
of longitude 174 30' E., the longitude found by chronometer from observation of star Canopus in 
latitude 41 S. The observation of star a Centauri is worked as an ex-meridian from the time 
deduced from longitude 174 30' E. Though the hour-angle in this case is a little over six hours, 
the latitude found is perfectly correct. 

4-0 SO 175' 



fO 



20' 



to 



20 




Pos n 
4II72 S 
174 47 E 



a Centaur/ 



30 



174 "30' E 



40 



I75 C 



10' 



20' 



* As the logs for sines and tangents are practically the same for very small angles are (i) may be taken out from 
the log sine table to save calculating for the seconds. 



110 

SIMULTANEOUS^) OBSERVATIONS OF TWO DIFFERENT STARS BY 
THE OLD "SUMNER" METHOD. 

1898. Shortly after sunset on March 3rd, somewhere between the parallels 
of 51 15' N. and 51 50' N., a chronometer indicated mean time at Greenwich 
3d. 6h. 48m. 385. when the true altitude of # Procyon was 31 57' east of 
meridian; again, after running east (true) 3 m., a chronometer indicated 3d. 6h. 
59 m. 20 s. when the true altitude of # Capella was 83 50' east of meridian. 

Required the position of the ship at time of last observation, and the true bearing of 
the stars by Sumner's method of progression on the chart. 



IST OBSERVATION : # PROCYON TO S.En. 
T. alt. of # 31 57 E 



2ND OBSERVATION : 



D. H. M. s. 

M.T. Green. 3 6 48 38 
Sid. T. (G. noon) 2245 7-9 
Accl. + i 7-1 



Sid. T. Green. 



5 34 53'o 



#'s Dl. 5 29 N 

PD 84 31 N 



D. H. M. s. 

M.T. Green. 3 6 59 20 
Sid. T. (G. noon) 2245 7-9 
Accl. + i 8-9 

Sid. T. Green. 5 45 3 6'8 



CAPELLA TO S.En. 

T. alt. of * 83 50 E 

*'sDl. 45 54 N 



PD 



44 



6N 



Run between observations, East 375m. = d. long. 6-0* E 



A 31 57 
L 51 15 

84 3i 


Sec 0-203479 
Cosec 0-001992 

Cos 9-029332 
Sin 9-895988 


A 83 50 
L 51 i5 
P 44 6 

179 " 


167 43 


S 83 51* 
S - A 51 54* 


S 89 35* 
S - A 5 454 


H. M. S. 

#'s H.A. - 2 52 33-0 E 
*'sR.A. 7 34 0-3 


H. M. S. 

*'sH.A. - o 18 34-6 E 
K's R.A. 5 9 11-4 


Sin2 9-130791 


Sec 0-209046 
Cosec 0-001992 

Cos 9-008278 
Sin 9-897712 


Sid. T. Sp. 4 41 27-3 
Sid. T. G. 5 34 53'0 


Sid. T. Sp. 4 50 36-8 
Sid. T. G. 5 45 36-8 


Long, in T. o 53 257 


Long, in T. o 55 o-o 


Long 13 21' 25" W 
Run 6 o E 


Long. C 13 45' o" W 


A 8 3 50 
5i 50 
P 44 6 


Long. A 13 15 25 W 


A 31 57 
L 51 50 
P 84 31 


168 18 


179 46 

S 8953 
S - A 63 


S 84 9 
S - A 52 12 

H. M. S. 

* 's H.A. - 2 49 42-3 E 
*'sR.A. 734 0-3 

Sid. T. Sp. 4 44 18*0 
Sid. T. G. 5 34 53-0 


H. M. S. 

#'s H.A, - o 10 14-4 E 
K's R.A. 5 9 11-4 

Sid. T. Sp. 4 58 57'o 
Sid. T. G. 5 45 36-8 


Sin2 9-117028 

Sumner: Lat. 51 27^' 
ip: Lat. 51 32' N., lonj 


Long, in T. o 50 35-0 


Long, in T. o 46 39-8 
Long. D 11 39' 57" W 


Long. 12 38' 45" W 
Run 6 o E 

Long. B 13 32 45 W 


N., long. 13 o' W. 
?. 12 55' W. 


Position of ship by 
True position of sh: 



Sec 0-20348 
Cosec 0-15745 



Cos 
Sin 



7-85289 
9-00144 



Sin2 7-21526 



Sec 0-20905 
Cosec 0-15744 



Cos 
Sin 



7-30882 
9-02283 



Sin2 6-69814 



Bearing of * Procyon, S. 53 E. ; and bearing of * Capella, S. 24 E. 
(a) Practically though not absolutely simultaneous. 

NOTE. This is the problem (b) of the Board of Trade Examination for Extra Master, with the excep- 
tion that as set for that examination both observations are taken at the same instant, only one chronometer 
time being given. As this is probably never realized in practice, the more usual experience of having a few 
minutes' interval between the observations is here given. 







(Azimuth 



Ill 



SIMULTANEOUS ( a ) OBSERVATIONS OF TWO DIFFERENT STARS BY THE 
IMPROVED "SUMNER" METHOD. 

1898. Shortly after sunset on March 3rd, in latitude by D.R. 51 15' N., longitude 13 40' W., a 
chronometer indicated mean time at Greenwich 3d. 6 h. 48m. 383. when the true altitude of 
# Procyon was 31 57' east of meridian; again, after running east (true) 3fm., a chronometer 
indicated 3d. 6h. 59 m. 20 s. when the true altitude of # Capella was 83 50' east of meridian. 

Required the position of the ship at the time of last observation, and the true bearing of each 
star at the time of their observation. 



IST OBSERVATION : > 

H. M. s. 

M.T. Green. 6 48 38 

Sid. T. (G. noon) 2245 7-9 
Accl. + i 7-1 



Sid. T. Green 5 34 53' 



PROCYOX TO S.Eo. 

T. alt. of X 31 57 
*'sDl. 5 29 N 

P.D. 84 31 N 



Run between observations, East 3-75 m.= d. long. 6'o' E. 



3i 57 
5i 15 
84 3i 

167 43 



Sec 0-203479 
Cosec 0-001992 



S 81 
S- A 5~i 


;5i* 
54* 


Cos 9-029332 
Sin 9-895988 


^ 

i -19 S 


*'sH.A. 
*'s R.A. 

Sid.T. Sp. 
Sid.T.G. 

Long, in T. 
Long. 


H. M. S. 

2 52 33-0 E 
7 34 0-3 


Sin3 9-130791 


Lat. 5 iJ \ A 
* Procyon I B 

H. M. 1 

H.A. 2 52 ) C 


4 4i 27-3 
5 34 53'o 

o 53 257 


13 21' 25" W 



Long, (i) 1 3 1 5' 25" W 

H. M. s. 
Long, in T. o 53 1-7 



Gives Az. S 53*3 E and 
Pos.-line N 36-7 E 



2ND OBSERVATION : X 

H. M. s. 

M.T. Green. 6 59 20 
Long, in T. o 53 1-7 W 



CAPELLA TO S.Eo. 

I 



T. alt. of * 
Z.D. 



50 Sd 
10 



M.T. Sp. 6 6 18-3 

Sid.T. (G.noon) 22 45 7-9 



Accl. 

Sid. T. Sp. 
*'sR.A. 

*'s H.A. 

Dec. 

Alt. 

Az. 

Pos.-line 



i 8-9 



28 52 35-1 

29 9 11-4 

o 16 36-3 E Sin 8-8595 



45 54' 
83 50' 



Cos 
Sec 



9-8426 
0-9689 



S 27 57' E Sin 9-6710 
N62E. 



LAT. BY EX-MER. TABLE No. 3 OF BLACKBURNE'S AND 
WESTLAND'S TABLES. 



H. M. o < 

H.A. o 16-6) Cor. + 4-5 
Dec. 45 54' N J 45 54 



Arc (i) 
Arc (2) 
Lat. 



Alt. 83 50 ) Cor. - 43 
Az. 27 57) Z D 6 zoN 



45 58'5' N 
5 57 N 
51 25-5' N 



Arc (2) 



557N 



ist obsn. X 's Az. S 53'3E gives lat. error from Table M -84 N to E at lat. 51 15 N 
2nd obsn. #'s Az. S 28 E gives lat. error from Table M -33 N to E at lat. 51 25-5 N 



FIGURE. 



Lat. error -51 



diff. lat. 10-5 



long, 
ro' 



long. cor. 
20-6' E. 



Lat.S/^SS'/f. B 




Long. 
Cor. 



13 i5'4 W 
20-6 E 



Long, in 12 54*8 W 



Lat. 
Cor. 



51 25-5 N 

6-8 N 



Lat. in 51 32-3 N 



Long. cor. 20*6 x -33 



618 
6-18 

6-798 N 



Lat. cor. 



NOTE. This example illustrates very forcibly 
the superiority of the improved Sumner method 
over the old Sumner method which the Board 
of Trade so tenaciously hold on to in their 
examinations. By the old method the work is 
about twice as long, requires the aid of a chart, 
and gives a result 4^' in error in the latitude and 
5' of error in the longitude. By the improved 
method no chart is required (though it may be 
used if preferred with the same result), and the 
position is less than ' in error in either latitude or 
longitude. 

The Marcq St. Hilaire method of calculation 
gives 2' of error in latitude and 2' in the longitude. 



(a) Practically though not absolutely simultaneous. 



112 



IMPROVED "SUMNER" POSITION FROM TWO STELLAR OBSERVA- 
TIONS 

(COMBINING CHRON. LONG. OBSERVATION WITH AN EX-MERIDIAN BELOW THE POLE). 

1898. Soon after sunset on 25th December, at about 8 h. 2m. p.m., in latitude by 
D.R. 46 S., and longitude 164 30' E. Suppose the following observations: 

M. T. Green. 21 h. i m. 20 s. when T. alt. of # Sirius was 28 26' E. of meridian. 

M. T. Green. 21 h. ym. 26s. when T. alt. of a Crucis was 20 45' E. of meridian. 

Run in interval between observations, S. 80, E. i m. = dep. 0-98' = d. long. 1-4' E. 
Required the position of ship at time of second observation. 



IST OBSERVATION. 

H. M. s. 

M. T. Green. 21 i 20 Dl. of # Sirius. 

Sid. T. (G. noon) 18 12 8-3 , 

Accl. 3 27-2 16 35 S 



Sid. T. Green. 15 16 55-5 P.D. 73 25 



SIRIUS TO N.Eo. 



S 

S - A 



*'sH.A. 
*'s R.A. 



28 26 
46 o 
73 25 

147 5i 

73 55i 
45 29 J 

H. M. S. 

- 4 23 59 E 
6 40 44 



Sec 0-158229 
Cosec 0-018451 



Cos 
Sin 



9-442316 
9-853180 



Sin2 9-472176 



Sid. T. Sp. 2 16 45 
Sid.T. Green. 15 16 55-5 

Long, in T. 10 59 49-5 



46 N 
33 S 



C2 -13 N 



Long. 
Run 



164 57' 22" E Pos.-line N 7jW 
i 24 E == 



Long, (i) 164 58 46 E = xoh. sgm. 555. 

at time of 2nd 

obsn. 



-46 



16450 



165 



2ND OBSERVATION : * a CRUCIS. 

H. M. s. 

M. T. Green. 21 7 26 
Long. E + 10 59 55 



H. M. s. 

Sid.T. (G. noon) 18 12 8-3 
Accl. + 3 28-0 



M. T. Sp. 8 7 21 
M.Q'sR.A. X 8 15 



36-3 



M. Q's R.A. 18 15 36-3 



Sid. T. Sp. - 2 22 57-3 
#'s R.A. 12 20 59-6 

*'sH.A. - 9 58 2'3E 

12 O O 



H.A. 
Lat. 



H. M. , 

9 58) A 1-76 S 
46 S [ B 3-80 S 



Supt. 



I 58 



a Crucis j C 5-56 S 
gives Az. S i4 0< 5 E 



Table C2 gives Posn.-line for Plane Chart, S 79^ W 



FOR LATITUDE BY EX-MERIDIAN TABLE No. 3 OF 
BLACKBURNE'S AND WESTLAND'S TABLES. 



Decl. 
H.A. 



Alt. 
Az. 



6232'S 
2h 2 m. 



20 45 S 
14 30 S 



Arc cor. - 3 20-3 
P D 27 28-0 S 



P- M5 



Arc (i) 



Arc cor. 

Alt. 



Arc (2) 

r, (I) 



Lat. 



24 77 S 



- o 37-3 

20 45-0 S 

21 22-3 S 
24 7'7 S 

45 30-0 S 



TABLE 



RULE FOR USE OF EX-MERIDIAN 

No. 3. 
With Hour-angle from Lower Meridian. 

With declination and hour-angle take out 
arc reduction ; subtract this reduction from 
PD for arc (i). 

With altitude and azimuth take out 2nd 
arc reduction ; add this reduction to altitude 
for arc (2). 

Arc (i) + arc (2) = latitude. . 



* Sirius with latitude 46 S. gives longi- 
tude 164 58' 45" E., and position-line for 
plane chart N. 7^ W. 

* a Crucis with longitude 164 58' 45" E. 
gives latitude 45 30' S., and position-line 
S. 80 W. 

Chart position: Latitude 45 30-7' S., 
longitude 164 55' E. 

High-declination stars, such as a Crucis, 
are very useful for ex-meridians, as, if the 
time is only approximately correct, the lati- 
tude will not be far from the truth if the 
body is within an hour from the meridian 
below the Pole. 

In this example, notwithstanding that the 
star a Crucis is over 2 hours from the lower 
meridian passage, i m. of error in the time 
used for ex-meridian would only make 2^' 
of error in the resulting latitude. 



113 



THE SUPERIORITY OF STELLAR OVER SOLAR OBSERVATIONS. 

The two great advantages of stellar over solar observations are (i) that by the stars 
the latitude and longitude can be obtained simultaneously, instead of having an interval 
of three or four hours between the observations as is often the case when the sun is 
used, and (2) that uncertain errors in altitude resulting from personal equation, arc 
errors of sextant, or exceptional refraction may be practically eliminated by a proper 
choice of stars. If meridian altitudes can be obtained about the same time to the north 
and south of observer, it will be apparent to any one that the errors would be eliminated 
by taking the mean result of the two observations for the true latitude ; and in the same 
way the true longitude would be found by the mean result of observations taken nearly 
east and west of meridian. But it may happen that stars are not to be found north, 
south, east, and west of observer during the short time that the horizon is good for 
observation. The following is the plan that the writer used for several years with great 
success : Take three stars, and of these choose two on the same side of the meridian 
northward and southward of the observer for a good latitude. If they both happen to be 
the same distance from the meridian, as in the following example, 10' of error in the 
altitude will make practically no difference in the resulting latitude as found by the 
" Sumner " or double-altitude problem. Then choose another star on the other side of 
the meridian, as near as possible the same distance from the meridian; calculate the 
longitude with the latitude found from the previous observations, and the true longitude 
will be obtained by taking the mean between the eastern and western stars worked with 
the correct latitude. 

Elimination of Errors in Altitude. 

Diagram showing how the true latitude may be found by the "Sumner" 
method even when altitudes have been observed by a sextant with large unknown arc 
errors. 



i E 



Beielgtitse. 




152" 



40' 



See \vorked-out example from which this is taken on the following two pages. 



114 

POSITION OF SHIP FROM OBSERVATION OF THREE STARS, 

THEREBY ELIMINATING ERRORS IN POSITION RESULTING FROM UNKNOWN ERRORS IN 

ALTITUDE. 

1898. On March i8th, at 8 h. n m. p.m., A.T. at ship, in latitude by D.R. 44 32' S., 
longitude 152 20' E. Required the position of ship from the following observations : 

O , D. H. M. S. 

(1) # Achernar's corrected alt. 33 27 W of mer. when chron. showed M. T. Green. 17 22 5 50 

(2) X Betelguese 30 13 W 17 22 9 33 

(3) # /3 Centauri 38 32 E 17 22 12 17 

Ship making a true east course at speed of 12 miles per hour. 



(i) Decl. 



P. D. 



57 45 17 
90 o o 



32 14 43 



(2) Decl. 



7 23 16 N 
90 o o 



P. D. 97 23 16 



(3) Decl. 



P. D. 



59 52 58 S 
90 o o 

30 7 2 



SID. T. (G. NOON). 



Sid. T. Green. 21 49 47-47 



SID. T. (G. NOON). 



Sid. T. Green. 21 53 31-07 



SID. T. (G. NOON). 



1 7th 
Accl. 22 h. 5$m. 

Cor. Sid. T. 
M. T. G. 


H. 

23 

+ 


M. 

40 

3 


S. 

19-67 . 

37-8J 


Accl. 22 h. 94 r 

Cor. Sid. T. 
M. T. G. 


H. M. 
23 40 

n. + 3 


S. 

19-67 . 

38-40 


Accl. 22 h, 

Cor. Sid. 
M.T. G. 


i2^m. 
T. 


H. 

93 

t 

23 

22 


M. S. 
40 19-76 

3 38-86 

43 58-53 
12 17 


23 

2.2 


43 

5 


57-47 
5' 


23 43 
22 9 


58-07 

33 



Sid. T. Green. 21 56 15-53 



ACHERNAR TO S.WD. 



# BETELGUESE TO N.WD 



A 
L 
P 

S 

S-A 

*'sH.A. 
*'s R.A. 

Sid. T. Sp. 
Sid. T. Green 

Long, in T. 

Longitude 
Run 


33 27 
44 32 
32 15 

101 14 
55 7 

21 40 
H. M. S. 

6 25 18-5 W 
i 33 54'4 


Sec 0-147006 
Cosec 0-272772 

Cos 9V57326 
Sin 9-567269 


A 
L 
P 

S 
S-A 

*'s H.A. 
*'sR.A. 

Sid. T. Sp. 
Sid. T. Green 

Long, in T. 

Longitude (2) 
(D 


30 13 
44 32 
97 23 

172 8 

86 4 
55 5i 

H. M. S. 
2 II 41-6 W 

5 49 40-6 


Sec 0-147006 
Cosec 0-003616 

Cos 8-836297 
Sin 9-917805 


Sin^ 9'744337 


Sin'-i 8-904724 


A -ii S 
B 1-59 S 

C2 1-70 S gives 


A 1-52 N 
B 1-24 N 

C2 I76N gives 


7 59 12-9 
. 21 49 47-5 

10 9 25-4 


8 I 22-2 

. 21 53 31-1 


10 7 51-1 


152 2l' 21" E 

i o E 


Pos -line S 59 J E 


151 57' 46" E 

152 22 21 E 


Pos.-lineN6o>E 


_M__ 



Long, (i) 



152 22 21 E 



Dift. long. 



24 35 = 24-6' 



*'sH.A. 
*'sR.A. 



/3 CENTAURI TO S.ED. 



38 32 
44 25 
3Q 7 

"3 4 

56 32 
18 o 

H. M. S. 

- 5 48 45-3 E 
13 56 41-2 



Sid. T. Sp. 
Sid. T. Green. 



7 55'9 
56 15-6 



Sec 0-146138 
Cosec 0-299502 



Cos 
Sin 



9-741508 
9-489982 



Sin'-i 9-677130 



05 N 
t-73 S 



Long, (i) cor. = 1-70 S to E 
Long. (2) cor. = 176 N to E 

D. long. 3-46 : d. long. 24-6 : : lat. i : lat. cor. 7-1 N 



Long, in T. 10 ii 40^3 

Long. 152 55' 5"E Pos. -line 859-2 W 



C2 1-68 S gives 



Lat. used 
Cor. 



Lat. in 



Long, (i) 
7-1' x 1-7' 

Long, in 

Run in interval 

Long. 



44 32 o .S 
7 6N 



152 22 21 E 

12 4 W 



152 10 17 E 

45 E 



152 ii 



2 E when ft Centauri 
observed . 



Long, by W star 
E star 



152 55 5 E 
152 n 2 E 



2) 304 66 7 
by mean ot obsns. 152 33 3 K 






115 

POSITION OF SHIP FROM OBSERVATION OF THREE STARS. 

(This is previous example worked with 10' less altitude for each star. Result the same.) 

1898. On i8th March, at 8h. u m. p.m., A.T. ship, in latitude by D.R. 44 32' S., 
longitude 152 20' E. Required the position of ship from the following observations : 

, D. H. M. S. 

U) # Achernar true alt. 33 17 W. of mer. when chron. showed M. T. Green. 17 22 5 50 

(2) * Betelguese 30 3 W. , 17 22 9 33 

(3) # Centauri 38 22 E. , 17 22 12 17 

Ship making a true east course at speed cf 12 miles per hour. 




2) Decl. 



7 23 i6K 
90 o o 

97 23 16 



(3) Decl. 



59 52 58 S 
90 o o 

30 7 2 



Sru. T. (G. NOON). 



Sid. T. Green. 21 49 47-47 



SID. T. (G. NOON). 



SID. T. (G. NOON). 





H. 


M. 


S. 




H. 


M. 


s. 




ft. 


M. 


S. 
I9'67 


Accl. 22 h. 5^ m. 


+ 


3 


37-80 


Accl. 22 h. 9^111. 


+ 


3 


38-40 


Accl. 22 h. i2jm. 


+ 


3 


38-86 


Cor. Sid. T. 
M. T. Green. 


23 

22 


43 
5 


57-47 
50 


Cor. Sid. T. 
M. T. Green. 


^3 
22 


43 
9 


58-07 
33 


Cor. Sid. T. 
M. T. Green. 


23 

22 


43 

12 


58-53 
17 



21 53 3i'07 



Sid. T. Green. 21 56 15-53, 



ACHERNAK TO S.Wl). 



BETELGUESE TO N.Wo. 



A 

P 

S 
S- A 

K's H.A. 
*'s R.A. 

Sid. T. Sp. 
Sid. T. Green. 

Long, in T. 

Longitude 
Run 


33 17 
44 32 
32 15 


Sec 
Cosec 

Cos 
Sin 

Sin* 

A 
B 

C* 


0-147006 
0*272772 

9758230 
9-568856 


A 
L 
P 

S 
S- A 

*'sH.A. 
*'s R.A. 

Sid. T. Sp. 
Sid. T. Green 

Long, in T. 
Longitude (i) 

(2) 


30 3 
44 32 
97 23 


Sec 

Cosec 

Cos 
Sin 

Sin2 

A i 
B 


o - 147006 
0-003616. 

8-845387 
9-918233 


no 4 

55 2 
21 45 

H. M. S. 

6 26 46 9 W 
i 33 54'4 


171 58 

85 59 
55 5<> 


H. M. S. 
2 13 II-2 W 

5 49 40-6 


9-746864 


8-914242 


12 S 

I59S 


'SON 

24 N 


. 8 o 41-^ 
21 49 47'5 


8 2 51-8 
21 53 3*'i 


10 10 53-8 


1-71 S gives 


10 9 20-7 


C2 I 


74 N gives 


152 43' 27" E 
i o E 


Pos.-lineS59-6E 


152 20' 10" E 
152 44 27 E 


Pos.-lineN6o tE 




- 








Long, (i) 



152 44 27 K 



Dift. long. 



24 17 = 24-3' 



/3 CKNTAURI TO S.ED. 



A 
L 
P 

S 
S- A 

-*'sH.A. 
*'s R.A. 

Sid. T. Sp. 
Sid. T. Green 

Long, in T. 
Long. 

Long, 


38 22 
44 25 
30 7 


Sec 0-146138 
Cosec 0-299502 

Cos 9-742462 
Sin 9-491922 


Long, (i) cor. 171 
Long. (2) cor. 1-74 

D. long. 3-45 

Lat. used 
Cor. 

Lat. in 

Long, (i) 
7-04' x 1-71 

Run in interval 
Long. 


StoE 
NtoE 

:d. long. 24- 

44 32 o S 
7 o N 


3' : : lat. i': lat. cor. 7-04' 


112 54 


56 27 

18 5 

H. M. S. 

5 50 12-8 E 
3 56 41-2 

8 6 28-4 
. 21 56 15-5 


Sin'-i 9-680024 

152 33 A K 
152 33 10 E 


44 25 o S 


152 44 27 E 
12 2 W 


10 10 12-9 
152 33' H" E 

by W star 
E star 


152 32 25 E 
45 E 


when Centauri was 
observed . 

tudes, the longitude 

rlo At -' .CJ r<vtilH 


152 33 ro E 


With the above correct alti 



by mean of obsns. 152 33 12 E 



be practically the same by all three stars. 



116 

EXAMPLES TO FIND STARS SUITABLE FOR DETERMINING POSITION 
BY SIMULTANEOUS ALTITUDES. 

EXAMPLE i. 

1898. On 22nd February, at about 5h. 30 m. p.m., in lat. by D.R. 49 20' N., 
long, 8 45' W. Find what stars not less bright than mag. 0-5 are suitable for 
determining the position of ship by simultaneous altitudes. 



H. M. 
22 24 

Sp. +5 30 



A. O's R.A. 22 24 

A. T. Sp. + 



H. M. H. M. H. M. 

K..A. tner. 3 54 3 54 . . ? S4 ^ s-t 

X Capella R.A. 59 x Rigel 5 10 'x Sirius 6 40 X Procyon 7 34 

X's H.A. i 15 E H.A. i i6E H.A. 2 46 E X's H.A. "T^o E 

R.A. mer. +24h. 2754 The only stars of this magnitude (not including 

*-Vega l8 33 planets) which would be above the horizon would be 

*''s'H.A. ~g~2iW Capella, Rigel, Sirius, and Procyon east of meridian. 

= and Vega to the west. 

Rigel and Capella, having nearly the same R.A. and a large difference in de- 
chhation, will always make a good cut with one another ; also, position-lines from 
Vega and Capella will nearly always cross one another at a good angle in the Northern 
Hemisphere, as these stars are about loj hours apart in R.A., and in high northern 
latitudes they both remain almost continuously above the horizon. In this case either 
Capella or Procyon, worked for longitude, would make a good cut with any of the other 
three stars, which would be nearer the meridian than the prime vertical, and could 
therefore be worked for latitude, Rigel and Sirius being to the south and Vega to the 
north . 



EXAMPLE 2. 

1898. On 25th June, at about 5h. p.m., in lat. by D.R. 40 S., long. 171 E. 
Find what stars not less bright than mag. 0-5 are suitable for determining the position 
of ship by simultaneous altitudes. 



H. M. 

6 16 
A. T. Sp. +50 



A. O's R.A. 6 16 

T. : 



... . . H. S. H. M. 

R.A. mer. 11 16 ii 16 n 16 

X Achernar R.A. i 34 X Rigel R.A. 5 10 X Canopus R.A. 6 22 

X's H.A. 9 42 W X's R.A. 6 6W X's H.A. 4 54 W 

H. M. H. S. H. M. 

R.A. mer. n 16 ii 16 . . ii 16 

X Sirius 6 41 X Procyon 7 33 X Arcturus 14 n 

X's H.A. 4 35 W X's H.A. 3 43 W X's H.A. 2 55 E 

It will be seen at once that Sirius, nearly on the prime vertical, and Achernar, 
near the meridian below the Pole, will give a splendid position. Canopus would also 
give a good longitude in combination with Achernar, or position-line from Procyon tc 
N.W. would cross well with Arcturus to N.E. Rigel, having a very small altitude, 
would probably not be seen. 

NOTE. The planets Venus, Jupiter, Saturn, and Mars make good daylight stars 
for observation. Venus, the brightest of all, is nearly always available for longitude 
either in the early morning or evening. The relative positions of the other planets 
with the sun vary continuously. 

! In the Northern Hemisphere Vega and Altair, or Rigel and Capella, nearly always 
pair well together : when the first pair are morning the other are evening stars, and 
vice versa. In the Southern Hemisphere Canopus and Sirius, or either a or /3 Centauri 
and Arcturus, make good pairs for determining positions. In higher latitudes, in place 
of Arcturus, Achernar will always make a good cut with either of the Centaurs. 



117 

DOUBLE-ALTITUDE POSITION BY SUN AND MOON. 
LONGITUDE BY CHRONOMETER, AND EX-MERIDIAN 3 HOURS FROM THE MERIDIAN. 

1898. On 2nd January, at about 3 p.m., A.T. at ship, observed altitude of moon's 
U.L. was 26 33' o" E. of meridian when chronometer showed M.T. Green. 3h. 48m. 
303., and observed altitude of sun's L.L. was 5 30' 45" W. of meridian when chrono- 
meter showed M. T. Green. 3 h. 53 m. 75. Latitude by D.R. 51 30' N., longitude 
12 20' W. Height of eye, 33 ft. Run in interval between observations, i m. on a trne 
S. 85 E. course = dep. i'o' = d. long. 1-6' E. 

Required the position of ship at time of second observation. 



Obsd. alt. of (T 26 33 oE 
r>ip33ft- - 5 39 

>6 27 21 

Semi-d. - 14 55 
App. alt. c[ 's centre 26 12 26 
C *HS' ! 5H * 
T. alt. d 's centre 26 59 5 


H. M. S. o 

I 's R.A. 4 h. 24033-3 a'sdecl. 4h. 20 
2-0355. x 11-5 m. 23*4 8-3" x 11-5 m. 


54 29 N 
i 35 S 


Cor. R.A. 2 40 9-9 Cor. decl. 20 


52 54 N 


Sid. T. (G. noon) 
Accl. 3h. 4 8Jm. 

M. O'sR.A. 


P. 

H. M. S. 

18 48 34-53 

+ 37'54 
1 8 48 12-07 


D. 69 


7 


6 


Obsd. alt. O 
33ft.T. E.~r 4 ' \ 
Jan. 4- -3 f 

T. alt. -0- 




5 
-f- 


30 45 W 
i 42 




^ 


5 


32 27 



A 
L 
P 

S 
S-A 

|s H.A. 

R.A. mer. 
M. O'sR.A. 

M. T. Sp. 

M. T. Green. 

Long, in T. 

Long. 
Run 

Long, (i) 


26 59 
5i 30 
69 7 

H7 3 6 


Sec 0-205850 
Cosec 0-029510 

Cos 9-445590 
Sin 9-862827 


911, M - S - 

O'sdecl. 22 53 42 S Eq. T 423-25 
14-0'' x 3-9 h. 55 i'i6s. x 3*9 h 4- 4'52 


Cor. decl. 22 52 47 S Cor. Eq. T. 4 27*77 


73 48 
46 49 


H. M. S. 

M.T.G. 353 7 
Long. W o 47 29-2 


Cosec 0-410276 
Sin 9-711306 
Sin 8-984840 


H. M. S. 

- 4 50 3-4 E 
h. 26 40 9-9 


Si"' 2 9'543777 

A -40 S 
B -40 N 


21 50 6'5 
18 48 12-1 


M. T. Sp. 3 5 37'8 


3 o 54'4 
3 48 30-0 


C -oogivesAz. N9oE 

H. M. S. 

= o 47 29 -2 


A. T. Sp. 3" i 10 Cos 9-847263 
O's decl. 22 52 47 Cot 0-37-1688 


o 47 35-6 


Arc (i) 30 57' 28" S Cot 0-221951 
T. alt. 5 32j' 
Arc 12) 82 39 34 N 


" 53' 54" W 
i 36 E 


ii 52 i8W 


Cos 9-106422 




Lat. 51 42' 6"N 





Position of ship = Lat. 51 42' N., Long. 11 52^' W. 

As the moon was on the prime vertical when the altitude was taken, the time 
deduced from this observation should be absolutely correct, and the latitude by ex- 
meridian of the sun will also be correct without any additional work. 



NOTE. The work of correcting the moon's semidiameter and horizontal parallax is 
not here shown. These elements should be taken from the Nautical Almanac (p. Ill) of 
the month, where they are given for Greenwich noon, and midnight, for every day of the 
year. For accuracy, a correction is necessary for the number of hours from noon or 
midnight, and also two other small corrections one for parallax, for the figure of the 
earth, and the other for moon's augmentation with increase of altitude. For sea 
observations these corrections can usually be made with sufficient accuracy at sight. 



118 

POSITION FROM TWO CHRONOMETER LONGITUDES BY SUN AND 

MOON. 

1898. On loth July, at about 8 h. 5 m. a.m., A.T. ship, the observed altitude of Q's 
L.L. was 35 12' 30" when a chronometer showed M. T. Green. 20 h. 45m. 405., and 
observed altitude of ([ 's U.L. was 39 47' 20" W. of meridian when the chronometer 
showed M. T. Green. 20 h. 481x1. 483. Latitude by D.R. 49 N., longitude 10 45' W. 
Height of eye, 28ft. Run in interval between observations, N. 80 E. 0-5' == d. lat. 
o'i' N. ; dep. 0-5' E. = d. long. 0-66' = o' 40" E. 



Obsd.alt.ofO 35 12-5 
Cor. Table E^8 ft. + 9-5 


O's Dl. nth 22 13 iN 
3 |h. x 19" + i 2 


Obsd. alt. of a 
Dip -28 ft. 

Semi-d.* 

App. alt. 
H.P. 56' 26' I 
Cor. RaperT. 39 j 

T. alt. ([ 's centre 


39 47 20 
- 5 13 


d'sR.A.2ih. 

II'2m. X 2'OS. 

Cor. R.A. 

a'sDl. 21 h. 
i ram. x 12-8" 

Cor. decl. 
P. D. 


H. M. S. 

o 44 6-65 

22-4 


T. alt. -0- 

Eq. T. nth 

h. x -355. 

Cor. Eq. T. 


35 22 


Cor. dec). 22 14 3N 


39 42 7 
- 15 36 


o 43 44-25 


M. S. 

5 5-67 
- i-i4 


P. D. 67 46 


O / it 

io 29 20 N 
- 2 23 


39 26 31 

+ 42 25 


H. M. S. 

Sid.T.(G.noon) 7 947-03 
Accl.2oh. 48! m. 4- 3 25-15 


io 26 57 N 


40 8 56 


5 4-53 


M. O's R.A. 7 13 12-18 





7933 3 



A 35 
P 67 


22 

o Sec 
46 Cosec 

8 


0-183057 
0-033553 


A 40 9 
49 o 
P 79 33 


Sec 
Cosec 


0-183057 
0-007265 


152 


168 42 


S 76 
S - A 40 


4 Cos 
42 Sin 


9-381643 
9-814313 


S 84 21 
S - A 44 12 


Cos 

Sin 

Sin'-s 

A 
B 

Cor. 
Cor. 


8-993222 
9-843336 


A. T. Sp. 
Eq.T. 

M. T. Sp. 
M. T. Green. 

Long, in T. 

Longitude 
Run 

Long, (i) 


H. M. S. 

4 4 30-4 E Sin2 


d'sH.A. 
([ 's R.A. 

R.A. Mer. 
M. O's R.A. 

M. T. Sp. 
M.T. G. 

Long, in T. 

Long, (i) 
Long. (2) 

Diff. long. 


H. M. S. 

2 32 17-4 W 
o 43 44-2 

3 16 i'6 

- 7 13 12-2 


9-412566 


9-026880 


19 55 29-6 

+54'5 A 
g 


648 

47 N 

i7StoW 


1-47 S 
30 N 


20 34'I 

20 45 40 C'-J 
o 45 6 


20 2 49'4 

20 48 48 


1-17 S to K 

1-17 S to E 
i7StoW 


o 45 58-6 


11 16' 30" W 
40 E 


ii29'39"W 
ii 15 50 W 


ii 15 50 W 


13 49 


d. long. 1-34 


""""""" 



1-34 ) 13-8' 



400 
402 



d. long. 1-34' : lat. i o' :: 
d. long. 13-8 : lat. cor. 10-3' S 



Lat. used 49 o oN 
Cor. io 188 

Lat. in 48 49 42 N 



A '// 



Long, (i) ii 15 50 W 
17' x 10-3' = i 45 W 



Long, in 




* See note on previous page about correcting moon's semidiamet-H- and horizontal parallax lot- 
Greenwich date. 






119 

EXAMPLES TO FIND THE ERROR AND DEVIATION OF THE COMPASS. 

(i.) BY SUN'S AZIMUTH. 

1903. On 231x1 June, p.m., at ship, in latitude 35 30' S., long. 175 o' E., when a 
chronometer which kept mean time at Greenwich showed 22 d. i6h. um. 395. the 
sun bore by compass N. 70 W. 

Required the true azimuth and error of the compass by the A, B, C, Azimuth 
Tables; and supposing the variation to be 13 30' E., required the deviation of the 
compass for the direction of the ship's head. 



I). H. M. S. o , M. S. S. H. 

M.T. G. ->2 16 ii 39 Peel. 23 278 Eq. T. i 42-8 -54 x 7-8 

Long. E + ii 40 o Cor. 4'2 

M.T.ship23 35139 Cor. Eq. T.I 38-6- M.T 

Eq- T. - i 39 = 



A. T. ship 3 50 o \ - H.A. West 



Lat. 35 30 S J A -45 N 

Decl. 23 27 X / B -51 N 



Cor. -96 N gives True Az. from Table C N 52 W 

Compass bearing N 70 W 

Error 18 E 

Var. i 3 J E 



Deviation 4^ E 



(2.) BY STAR'S AZIMUTH. 

1903. On i5th November, at about 3 h. 20 m. a.m., at ship, in latitude 39 30' S., 
longitude 177 30' E., when a chronometer (corrected) indicated mean time at Greenwich 
14 d. 3 h. 30 m. the star a 2 Centauri bore by compass S. 41 E. 

Required the true azimuth and error of compass by the A, B, C, Time Azimuth 
Tables; and supposing the variation to be 15 30' E., required the deviation of th& 
compass for the direction of the ship's head. 



1). H. M. S. H. M. S. 

M.T. G. 14 330 o Sid. T. (G. noon) 15 29 38-6 

Long. E 4- ii 50 o Accl. 3h. 3om. 4- 34*5 

M.T. ship 14 15 20 o M. Q's R. A. 15 30 13*1 

M. Q's R. A. + 15 30 13 ^_^__ 

Sid. T. ship 6 50 13 or R. A. of the meridian 
#'s R. A. 14 33 i 

A -39 S 
*'s H.A. 7 42 48 B 1-96 S 

Lat. 39 30' S Table C 2*35 S gives True Az. S 28-9 E 

# a Centauri Table B ) ^=^ Compass bearing S 41-0 R 

Error 12' i E 

Var. 15-5 E 

Deviation 3-4 W 

NOTE. The H.A. of a star is found by taking the difference between the S,id. T. 
at ship and the star's R.A. The H.A. is east when Sid. T. is least, and west when 
Sid T. is best. 



120 



EXAMPLES TO FIND THE CORRECT HOUR-ANGLE AND AZIMUTH WHEN TIME 
IS GIVEN IN NEW ZEALAND MEAN TIME. 



(i.) SUN'S AZIMUTH. 

1904. On 24th May, at 3 h. om. p.m., New Zealand mean time. Required the sun's true 
azimuth by the A, B, C, Azimuth Tables, at Nelson, in lat. 41 17' S. and long. 173 15' E. = 
ii h. 33 m. 



U. H. M. 

M.T.N.Z. 24 3 o 

Long. 170 30' E - ii 30 

M.T. Green. 
Long. Nelson' 

M.T. Nelson 24 3 3 

Eq. of Time + 3$ 

A. T. Nelson 24 3 6 



23 15 30 
+ ii 33 E 



's Decl., 23rd 20 24 ii N 

r. var. 29" x 15-5 h. = cor. 4- 7 30 

Cor. Decl. 20 31 41 N 



M. s. 

Eq. of Time 3 32-3. 

Hr.var.o'iSs. x 15-5 h. = cor. - 2'8 

Cor. Eq. Time 3 39-5 



Lat. 41-3 S \ A -84 N 

Decl. 20-5 N ' B -51 N 

H.A. 3h. 6m. j C 1-35 N gives O's true Az. N 44-7 W 



O's Azimuth by Burdwood's Tables, N 44'6 W 



(2.) SUN'S AZIMUTH. 

1904. On 23rd December, at 7h. o m. p.m., New Zealand mean time. Required the sun's true 
azimuth by the A, B, C, Azimuth Tables, at Wellington, in lat. 41 17' S. and long. 174 45' E. 



Long, for Standard time 172 30 E 
. Wellington 174 45 E 



or. for diff. of long. 



2 15 = + 9 m. to N,Z. M. time 



[NOTE. The Decl. and Eq. of Time may be taken out 
u sight with sufficient accuracy for azimuth purposes.] 



M.T. N.Z. 


D. H. M. 

23 7 o 






Cor. for long. 


+ 9 






M.T. at Wellington 
Eq. of Time 


23 7 9 


Lat. 
Decl. 




41-3 s 

23'SS 


A. T. Wellington 


23 7 10 


H.A. 


7h. 101 



\ A '28 S named S because H. A. is more than 6 h. 

I B-45S 

) C 73 S gives O's Az. S 6i- W 

O's Azimuth by Burdwood's Tables, S6ri W 



(3.) STAR'S AZIMUTH, 

1904. On i5th September, at 7h. 30 m. p.m., New Zealand mean time, in lat. 43 30' S. and 
long. 169 40' E. Required the true azimuth of star a Centauri by the A, B, C, Azimuth Tables. 



M.T.N.Z. 
Long. 172 30' E 

M.T. Green. 
Long. 169 40' E 

M.T. ship 
M.Q's R.A. 

Sid. T. ship 
*'sR.A. 

*'s H.A. 



D. H. M. S. 
15 7 30 O 
- II 30 O 

14 20 o o 
+ ii 18 40 

15 7 18 40 
+ ii 32 26 

18 51 6 
'4 33 i 



4 18 5W 



H M. S. 

Sid. T. (Green, noon) i4th 1129 8'8 
Accl. for 20 h. 4- 3 I7'i 



M. O's R.A. 



Lat. 43-5 S 
a Centauri 



32 25-9 



A '45 N 
B 1-95 S 



H.A. 4h. i8m. j C 1-50 S gives Azimuth S 4i'6 W 

True Azimuth by calculation, 842-55 



121 



GREAT-CIRCLE SAILING-COURSES. 

The initial great-circle courses between any two places on the globe comprised 
within the zones of latitudes 85 N. and 85 S. may be quickly determined by the aid 
of the A, B, and C Tables. (See rule and examples below.) 

RULE. Turn the difference of longitude between the two places into time, and 
consider this as the hour -angle ; with this H.A. and the latitude of departure as latitude, 
take out the factor from Table A, and with the latitude of destination as declination, 
enter Table B. Follow the same rules as for finding and naming the azimuth, and 
Table C (azimuths) will give the initial course. Reverse the process, and we have the 
course at point of destination. 

The following examples are taken from Norie's Epitome, so that it may be readily 
seen that there is no appreciable difference between the course as found by these 
tables and that obtained by the more rigorous and lengthy calculation which is 
generally used : 

Example (i). Required the great-circle initial courses between Cape Runaway, 
New Zealand, in latitude 37 31' S., longitude 178 i' E., and Cape Horn, in latitude 
55 59' S., longitude 67 16' W. 



H. M. 

H.A. 7 39 
Lat. 37$ o S. 
Decl. 56 o S. 



(i.) Lat. 37 31 S. Long. 178 i E. ) d. long 
(2.) Lat. 55 59 S. Long. 67 16 W. j 114 43 


H. 

' = 7 


M. S. 

38 52- 










H. M. 










A 


'35 


S. 


H.A. 


7 39 




1 A 


68 


S. 










O ' 










B 


1-64 


s. 


Lat. 


56 o 


S. 




84 


S. 


C 


1-99 


S. gives Co. S. 32^ E. 


Decl. 


37jo 


S. 


1 C 


1-52 


S. 



Course from Cape Runaway, S. 32^ E ; or from Cape Horn, S. 49^ W. 



Example (2). Required the initial great-circle courses between Otago, in latitude 

45 47' S., longitude 170 45' E., and Panama, in latitude 8 57' N., longitude 
79 31' W. 

(i.) Lat. 45 47 S. Long. 170 45 E. ) d. long. H. M. s. 

(2.) Lat. 8 57 N. Long. 79 31 W. ' 109 44' = 7 18 56. 



H. M. 
H.A. 7 19 

Lat. 45| o S. 
Decl. 9 o N. 



A -37 S. 
B -17 N. 
C -20 S. gives Co. S. 82 E. 



H. M. 
H.A. 7 19 

Lat. 9 o N. 
Decl. 45f o S. 



A -06 N. 
B 1-09 S. 
C 1-038. gives Co. S. 44iW. 



Course from Otago, S. 82 E. ; or from Panama, S. 44^ W. 



Example (3). Required the initial great-circle courses between a position off 
Lizard, in latitude 49 50' N., longitude 5 12' W., and 5 m. E. of Barbadoes, in 
latitude 13 6' N, longitude 59 20' W. 



(i.) Lat. 49 50 N. 
(2.) Lat. 13 6 N. 



Long. 5 12 W. ) d. long. H. M. s. 
Long. 59 20 W. j 54 8' = 3 36 32. 



H. M. 

H.A. 3 36 
Lat. 49 50 N. 
Decl. 13 o N. 



A -86 S. 
B -29 N. 
C -57 S. gives Co. S. 69'8 W. 



H.A. 
Lat. 
Decl. 


H. 

3 

13 
49 


M. 
36 


50 


-! 

N. J 


A 
- B 

C 


'17 S. 
1-46 N. 
1*29 N. gives Co. 


N. 



Course from Lizard, S. 70 W. ; or from Barbadoes, N. 38^ E. 



122 

EXAMPLES TO FIND THE ERROR OF COMPASS FROM BEARINGS OF 
THE MOON AND OF THE STAR POLARIS. 

(i.) BY MOON'S AZIMUTH. 

iSgS. On 6th January, at about gh. 46m. a.m., M.T. at ship, in latitude 72 N., 
and longitude 25 15' E., when a chronometer showed M.T. Green. 2oh. 5m. 35. the 
moon bore by compass N. 25 W. Required the moon's true bearing and the error of 
compass for the direction of ship's head. 

H. M. S. H. M. S. , 

M. T. Green, sd. 20 5 3 c'sR.A. 20 h. 54934 a 's decl. 20 h 26 o 28 N 

Long. E + i 41 o 2-2 s. x 5m. + n i"'86 x sm. = - 9 

M. T. Sp. 21 46 3 Cor. R.A. 5 49 45 Cor. decl. 26 o 19 N 

Sid. T. (G. noon) 19 o 24 == -^ 

Accl. 20 h. sm. + 3 18 

R.A. mer. 164945 H.A. nh. om. > A 11-5 N 

's R.A. 5 49 45 Lat. 72 N B r88 N 

Decl. 26 N } o 

d'sH.A. ii o oW ) C 13-38 N gives Az. N 13-6 W 

Compass bearing N 25*0 W 
Error 11-4 E 

(2.) BY STAR POLARIS AZIMUTH. 

1906. On 6th February, at ich. 30 m. p.m., A.T. at ship, in latitude 25 N., 
longitude 35 45' E. Suppose * Polaris bore N. 4 E. Required the error of com- 
pass for the direction of ship's head. 

H. M. 

A Q's R.A 21 18 Lat. 25 N. ) 

#'s R.A. + (24h.) 25 25 H.A. 6h. 23m. gives Az. N 1-3 W. 

Table G., p. 88 ) 
A.T. of x-'s mer. pass. 4 7 
A.T. at ship 10 30 Compass bearing N 4 - o E. 

#'s approximate H.A. 6 23 W Compass error 5-3 W. 



ILLUSTRATIONS TO SHOW HOW LIVES AND SHIPS MAY BE SAVED 
BY THE CAREFUL OBSERVER, AND, CONVERSELY, HOW LIVES 
MAY BE LOST. 

As it has been the duty of the writer for the last few years to carefully go over all 
the evidences in connection with strandings, &c., on the New Zealand coast, he has 
been more than ever impressed with the value of keeping up regular systematic bear- 
ings and astronomical observations. Personally, he has known the comfort and benefit 
of doing so by several years' experience, and of late has many times noted the sad 
consequences of neglect to do so. 

As an illustration, let us take the case of a barque which stranded a few years 
ago, about u miles south of Kaipara Harbour. She was bound to Kaipara 
Harbour from Sydney in ballast, and at noon was about 143 miles from Kaipara 
Heads, with a fresh fair wind for her port. Towards evening (the weather apparently 
still fine) the barometer began to fall, and at 3 a.m. the wind had increased to gale 
force from W.S.W. Shortly afterwards land was seen, estimated to be 6 to 8 miles off. 
The land sighted was considerably to the southward of Kaipara Harbour, and the 
ship being in ballast it was impossible to beat off the coast to make either Kaipara 
or Manukau Harbours ; there was therefore nothing left to be done but to run the ship 
on the softest spot on a lee shore. Now, had the master of this vessel been in the habit 
of getting the ship's position shortly after sunset by stellar observations, he would in all 
probability have been able to get a very accurate determination of the ship's position at 
about 7 p.m., or a little later, when only 50 miles or less from the range of Kaipara 
light, which he could then have steered for with confidence, and a certainty of making ; 
and, as it happened to be H.W. at about 2 a.m., he would have had everything in his 
favour for an easy run into the harbour. 



123 

Another case was that of a large passenger steamer which was wrecked on 
the Three Kings a disaster which caused the loss of many lives. So far as we 
are able to gather from the evidence given at the inquiry, the weather was fine, 
on the evening before the disaster, and in all probability the position of the ship 
might have been very accurately determined at about 7 p.m., when the ship was 
about go miles in advance of the noon position. Such an observation would most 
likely have shown which way the current was setting, and many lives would have been 
saved. 

The third case within three years which has come before the New Zealand 
Courts in which a ship has been totally lost, but would in all human probability 
have been saved had the master taken stellar observations before dark, was that 
of a barque (2,192 tons) which was wrecked on Palmerston Island, Cook Islands. 

At noon on 6th November observations were taken which showed that the 
South Point of islands bore S. 52 W. 98 miles, and north end bore S. 55 W. dis- 
tant 95 miles. The ship was then on port tack, wind S.S.E. (true). The Captain 
then decided to go to leeward of the islands, and kept away a point. At 4 a.m. 
the look-out reported land on the starboard beam, and almost immediately after- 
wards the ship was on the reef. 

From the evidence it was stated that the sky was clear at that time, so that 
there is little doubt but that a position obtained by stellar observation at about 
7 p.m. would have shown the master how the current was setting, and enabled 
him to set a safe course to go clear of all dangers. 

A fourth and more recent case was that of an auxiliary schooner which was 
stranded and wrecked on Minerva Reef in about 24 south latitude in June, 1915. 

At 4 p.m. an observation was taken which made the ship to be 5 or 6 miles 
to westward of D.R. longitude from the noon position, but the master stated that 
he did not place much reliance on this observation. 

Had the master been conversant with the problem of determining his position 
by two stars he could no doubt have got an accurate latitude and longitude simul- 
taneously at twilight, at about 5.30 p.m., about two hours before the time when 
the ship was wrecked. 

Since the loss of some of the vessels just mentioned I have received the more 
cheering news of the probable salvation of two large steamers owing to the master, or 
his officers, taking stellar observations, and so being warned in time of a dangerous 
set by an unusually strong current. The captain of a large liner of over 7,500 tons 
gross register wrote to the author in March, 1906, as follows : " During my ten 
years of command I have always used your tables for sun and star navigation, 
and invariably with excellent results and great success. In one instance particularly 
(of which I send you the working) it saved me from a narrow escape off Lincoln 
Island (northern extreme Island of Paracel group). Having experienced unusually 
strong currents setting to westward I kept well over to Macclesfield Bank, but 
nevertheless I took good observations in the morning and obtained cross bearings 
of stars, and was able to alter my course in time. Another shipmaster expressed 
gratitude that these tables had taught him the value of stellar observation, as 
such observations had been the means of saving his ship from stranding in. the 
Bay of Bengal." 

VALUE OF TWILIGHT STELLAR OBSERVATIONS. 

Twilight (a few minutes after sunset, or a few minutes before sunrise) is far 
and away the best time out of the twenty-four hours for reliable observations. The 
horizon at that time is generally very clearly denned, without any glare, requiring 
no shades for the sextant, and two or three of the brightest stars with a suitable 
difference of bearing between them can often be observed, which will give a perfect 
position in both latitude and longitude at practically the same instant of time. 
The writer having made a regular practice of taking these observations for several 
years of his sea life knows well from experience that no other observations are to 
be compared with them. The noon position is as best only an approximation, 
and should never be relied on too implicitly, for though half a dozen men may 
take the meridian altitude and get the same result they may all be several 
miles in error, owing to some unusual excessive refraction near the horizon. 
The very agreement of so many observers would only give a false confidence, which is 
the more dangerous as there is no opportunity with the sun observation (except when 
near land) of checking it, and thereby determining the error. Then, again, the so-called 
noon longitude generally depends on an observation taken at about 8 or 9 a.m., 
and the calculation of the time from this observation is often made with an erroneous 



124 

latitude, thereby giving a wrong result; and currents, or bad steering, &c., may again 
combine to still further throw the position out. With the position, however, obtained 
by simultaneous observations of two or three stars, errors resulting from uncertainty of 
refraction, &c., may be eliminated, and the position altogether should be much 
more accurate. 

POWER OF SHIPOWNERS AND BOARD OF TRADE TO MINIMIZE 

DISASTER. 

If shipowners made it compulsory for their officers to obtain the ship's 
position whenever possible by stellar observations at twilight, it would, I believe, 
be the means of saving many ships from disaster, and the saving of not a few 
lives ; also, if this problem were given in our Board of Trade examinations for 
master and mate it would help greatly in making our ship officers familiar with it, 
and to further encourage the more frequent observations of this very important 
problem we would advocate that short and accurate methods of solving the problem 
by the use of up-to-date tables for facilitating the work should be allowed in the 
examination. The problem is now given in the voluntary examination for extra 
master, but it is given in a very unpractical way, requiring two observers with 
sextants as well as an officer to take the time ; and the lengthy way in which it 
is required to be worked in the examination-room will be quite enough to deter 
most men from making anything like a daily practice of such an observation after 
their examination is over. To obtain confidence in the result of observations for 
any problem the navigator must make more than an occasional trial of it. 

VALUE OF COMBINED OBSERVATIONS OF MOON AND PLANETS WITH 

THE SUN. 

It may not be amiss here to remind navigators that when the moon is up in the 
daytime observations of moon and sun will also give both latitude and longitude 
at the same instant of time. Reference to example on p. 117, shows that the moon 
may often be observed on the prime vertical when, in the winter months, the sun 
never comes near to it. When the sun has a high south declination, the moon, 
when near the full, will have a high north declination, and vice versa, so that in the 
winter months it is especially good when in this quarter for longitude, and during the 
summer months for latitude. This observation, however, is even less frequently taken 
than that of simultaneous observations of two stars, as this problem is not given even 
in the extra masters' examination ; it also entails more work in the calculation, and the 
upper limb has often to be taken, which without practice is liable to be confusing. 
The planet Venus, too, may sometimes be utilized in the daytime. The writer has 
occasionally obtained the latitude from an observation of "Venus when on or near the 
meridian, at about 9 a.m., or 3 p.m., when the usual sights were taken for longitude. 
Captain W. P. Dawson, R.N., of H.M. surveying-ship " Penguin," has informed him 
that he has sometimes observed Jupiter, Sirius, and Canopus during the daytime. 
This must require good eyesight and a very clear atmosphere. The approximate 
altitude of the planet should, of course, be calculated, and the sextant set to it ; then, il 
the observer looks at the horizon in the direction of the meridian through a good 
telescope, he may see a little white speck near the horizon, which will be the reflected 
star. A pelorus set to the true north or south will be found helpful in directing to the 
spot where it should be seen. 

On the back of the United States pilot chart of the North Pacific Ocean for 
November, 1909, published by the Hydrographic Office of the United States of America 
Navy Department, some very interesting experiences of stellar observations during 
strong daylight were given by Captain R. E. Thomas, of the British steamer " Swedish 
Prince." He states that on the passage from New York to the Brazils noon observa- 
tions of Venus for longitude were made simultaneously with observations of the sun for 
latitude on fourteen dates, between September 2ist and October 8th, 1906. On another 
occasion, while on a passage from Rio to New York, similar observations were taken on 
sixteen dates, between February 8th and February a6th, 1907. Using Venus and 
Jupiter in conjunction with the sun while on the passage from Cape San Roque to Bar- 
badoes, in a current varying in strength and direction, he was able for a number of 
days to obtain four absolute positions in broad daylight during each day viz., about 
9 a.m., longitude sun, latitude Venus; about '10.30 a.m., latitude and longitude by 
observing Venus S.W. and sun S.E. ; at noon, latitude sun, longitude Venus W. : and 
about 4 p.m., latitude Jupiter, longitude sun. During these days the noon longitude 
obtained solely by the sun could not but be considerably in error. In concluding he 
says : "I may add that Jupiter, though not so easily observed as Venus, is still worthy 
of a place as an observable object by daylight, and one that will repay the patience and 
practice which its successful observing calls for." 



125 



EXAMPLE OF FINDING THE ERROR OF CHRONOMETER BY OBSER- 
VATIONS IN ARTIFICIAL HORIZON, 

SHOWING THE USE OF TABLE D IN WORKING OUT SEVERAL OBSERVATIONS SEPARATELY. 
1898. On i6th April, at about 7 h. 10 m. a.m., M.T. at place. Suppose the 
following observations to have been taken at Observation Spot, Suez Dock. Index 
error of sextant - o' 34". Lat. 29 56' 3" N., long. 32 33' 12" E. = 2 h. lorn. i2'8s. 



H. M. S. 

Approx. times at Green, by chron. 16-59 33 

16 59 57'5 

17 o 23 



Obsd. alt. O 



/ 

Required the error of chronometer 



47 

1 ii 

1 35'5 

2 O 



(I) 
(2) 

(3) 
(4) 
(5) 
(6) 
(7) 



39 38 40 

39 49 20 

40 o 20 
40 10 50 

4O 21 IO 
40 31 40 

40 43 20 



Alt. diff. 

10 40 

11 O 

10 30 

IO 2O 

10 30 

11 40 



M.T. G. 

From noon 6th 7h. 



D. H. M. s. 
5 17 o 47 
24 o o 



O's Dl. 10 13 5oN 
53-1" x 7h. 6 12 S 

Cor. Dl. \o 7 38 N 



M. s. 

Eq. T. o 16-65 

o'6s. x 7h. 4-2 



Cor. E. T. o 12-45 



.No. 4. Middle Sight 

Alt. O 40 10 50 

I.E. - 034 



P. D. 



79 52 22 



2)40 10 16 



S 
S- A 



H.A. 



20 18 35 
29 56 3 

79 52 22 

130 7 o 

65 3 30 
44 44 55 

H. M. s. 
4 49 12-3 



Sec 0-062182 
Cosec 0-006820 



Cos 9-624999 
Sin 9'847572 



Sin2 9-541573 



Table D. 

L. 30, Az. 90, gives 4-62 s. to i' alt. -^ 2 
= 2*31 s., because altitude is doubled 
in artificial horizon. 



App. lat. 20 
Ref. & par. - 



5 8 
2 30 



S. D. 



20 2 38 

+ 15 57 



T. alt. -0- 20 18 35 



A. T. Sp. 19 10 47-7 
Eq. T. - 12-4 



M. T. Sp. 19 10 35-3 
Long. E - 2 10 i2'8 

M. T. G. 17 o 52-5 
Chron. (4) 17 o 47-0 

Chron. fast o 24-5 



H. M. S. 

M.T. G. (No. 2) 16 59 32-9 
2-31 s. x io' - 24-6 

M.T. G. (No. i) 16 59 8-3 
Chron. 16 59 33-0 



Chron. fast 



A -198 
B -19 N 

C -oo gives Az. 90 



H. M. s. 

M.T.G.(No. 4 ) 17 022-5 
2*315. x ioj' - 24-2 



M. T. G. (No. 3) 16 59 58-3 
Chron. 17 o 23-0 



o 24-7 



Chron. fast 



M.T.G.(No. 4 ) 
2-315. x ioj' 



M.T. G. (No. 5) 17 o 46-4 
Chron. 17 i ii'o 




Chron. fast 



o 24-6 



M.T. G. (No. 3) 
2*31 s. x n' 

M.T. G.(No. 2) 
Chron. 

Chron, fast 



M. T. G. (No. 5) 
2*31 s. x ioj' 

M.T. G. (No. 6) 
Chron. 

Chron. fast 



H. M. s. 

16 59 58-3 
- 25-4 

16 59 32-9 
16 59 57'5 

o 24-6 




o 24-9 



H. M. S. 

M.T.G. (No. 6) 17 i 10-6 
2-315. x n' + 27 



M.T.G. (No. 7) i7 i 37'6 
Chron. 17 2 o - o 



Chron. fast 



O 22'4 



It is evident that the last observation was in error, probably 
owing to the altitude having been either read off or put down 
incorrectly. It is therefore rejected, and a mean taken of the 
other six. 



Results. 
Chron. fast 



s. 

24-7 
24-6 
247 
24-6 



Observations with artificial horizon are not so much needed as they were twenty 
or thirty years ago, as of late years time signals giving G.M.T. have been esta- 
blished at most places of importance. Still, it is well to be independent of such aids. 
In the first place, they are not always reliable, and, secondly, in these days of steam 
and rush a vessel sometimes arrives at and leaves a port again, as at Port Said, 
before the time when the signal is given ; and there are still many places where such 

aids are not to be found. The writer, when second officer, used sometimes to check Mean 24-66 

the chronometer by observations of stars in the quicksilver, in his middle watch at 

night, when tied up in the Suez Canal or at anchor in the Bitter Lakes. Results 

were very satisfactory, as proved by observations east and west of the meridian, which did not generally 
differ more than i s. from one other. 

He never found it possible to get such observations of the sun on board ship, as in the daytime so many 
people are moving about ; but in a large ship at anchor in smooth water observations in the quicksilver can 
often be taken at night, when all on board except the observer and time-taker are in bed, and everything is 
quiet. 

9 Azimuth. 



126 

REMARKS ON THE VALUE OF EQUAL ALTITUDES BY SEA. 

We would draw attention here to the value of the short equal-altitude problem, as 
this method of obtaining the longitude, though very simple and useful, is seldom 
noticed by nautical writers. The problem is more especially useful in the case of stars, 
owing to there being no appreciable change in a star's declination, and because suitable 
ones can generally be found in any latitude. Even on dark nights a very fair longitude 
can generally be obtained, errors of altitude eliminating one another in a similar way as 
when stars are observed for latitude north and south of the meridian. An equally good 
result is obtained if both altitudes are observed the same amount too great, or too small, 
as if they had both been correct, and the problem is so simple that it takes very little 
longer than to get the latitude by meridian altitude we mean, of course, when within 
the limits where correction for change of latitude and declination are not necessary. 

The writer has often taken these equal altitudes about the same time as other 
observations have been taken sometimes before daylight with an indifferent horizon, 
and at others with a good horizon a little before sunrise or after sunset and they have 
nearly always agreed splendidly with the star-position longitude obtained by double 
altitude. 

The navigator should not, however, use this method beyond its proper limits, and 
when the sun is observed it will seldom be useful except in the tropics, and then 
principally when running nearly due east or west, as on passages from Penang to 
Ceylon and Aden. When running due east or west no correction of altitude or time is 
required for ship's change of position, as she would change her longitude only by the 
portion of time which she gains or loses on the sun in the interval. Also, when the 
body observed bears east or west, no correction is required for several miles' change of 
latitude to the north or south ; therefore it follows that when the observed body is 
near the prime vertical, and the change of latitude is small, it is not practically 
necessary to make any corrections for change of ship's position. Table 29 in Raper 
gives the hour-angle and altitude of a body on the prime vertical ; and most other 
epitomes also have a table at any rate for giving the hour-angle of same, which is 
always useful for showing the best time to observe for longitude. 

(i.) THE COMPUTATION (Raper, p. 801). 

Take the mean of a.m. and p.m. times by chronometer : this, when the ship does 
not change her latitude, is the time by chronometer of apparent noon ; when the 
latitude changes, this time is the time of approximate noon. Apply chronometer error 
and equation of time (p. II., N.A.), which will then show the A.T.G.; the difference 
between that and the apparent noon at ship being the longitude in time. 

(2.) CORRECTION FOR CHANGE OF LATITUDE. 

With half the interval as an hour-angle, compute the azimuth. To the log. sine of 
half the D. lat. made good, add the log. sec. of the lat. and the log. cotan. of the 
azimuth ; the sum, rejecting tens, is the log. sine of the correction in time. 

When the ship has approached the sun or star in the interval, subtract this time 
from the above mean ; when she has receded from the sun, add it. The result is the 
time^by chronometer at apparent noon. 

NOTE. When the observed body is within 10 or so of meridian, the D. lat. made 
good in the interval may be added or subtracted from the altitude according as the 
ship has approached or receded from the sun, instead of going through the longer but 
more accurate computation. 

LONGITUDE BY EQUAL ALTITUDES OF THE SUN. 

EXAMPLE i. Ship steering nearly East or West. 

In lat. by D.R. 6 N. and G's decl. 5 N. Equal altitudes of the sun were taken 
when chronometer times, a.m. and p.m., showed respectively i8h. lorn. 363. and 
i8h. 42m. 52 s. Chronometer fast on G.M.T. lorn. 6s. Required the longitude. 

H. M. S. 

Chron. time a.m. 18 10 36 

Chron. time p.m 18 42 52 

2 ) 36 53 28 

Middle time by chron. 18 26 44 

Chron. fast - 10 6 



M. T. G. of Sp. A. noon 18 16 38 

Eq. T. - 3 34 

A. T. G. of Sp. A. noon 18 13 4 

A. T. Sp. 24 o o 

Long;, in. time 5 46 56 

Longitude 86 44' o" E 



127 

EXAMPLE 2. Where Ship has changed her Latitude between Sights. 
Using the preceding example, with course made good N. 73 E. ym. = D. lat. 2'. 

H. M. S. 

Halfintl. asH.A. o 16 8 , Half D. lat. ro' Sin 6-464 

Lat. 6 N Table A 1-50 S Lat. 6 Sec 0-002 

Decl. 5N B 1-25 N Az. 76 Cot 9-397 



Az. S76 C -25 S 15"= is. to add. Sin 5-863 

H. M. S. 

Middle time of observations by chron. 18 26 44 
Correction for change of latitude + i 



18 26 45 

Here the sun is to the southward and the course is to the northward, or the ship 
has receded from the sun. 

As the change in c 's decl. never exceeds' i' in an hour, the correction for this may 
be disregarded when observations are taken within a few minutes of noon. 

EXAMPLE 3. -Longitude by Equal Altitudes of a Star near the Meridian. 

* 1898. On 6th September, at about 5h. 26 m. and 5h. 36m. a.m., A.T. at ship, in 
lat. by D.R. 9 30' N., long. 63 E. Observed equal altitudes of * Aldebaran to the 
northward at 13 h. 49m. 55. and 13 h. 59m. 55. by chronometer which was fast of 
G.M.T. 37m. 365. Run in interval between observations, S. 75 E. 2 m. = D. lat. 0-5'. 

H. M. s. 

ist chron. time 13 49 5 

and chron. time 13 59 5 

2 ) 27 48 IO 

Chron. time of transit 1354 5 

Chron. error 37 36 

M. T. G. of transit 13 16 29 

Sid. T. (G. noon), 5th 10 58 2 '2 

Accl. for i3h. i6Jm. + 2107-8 

Sid. T. at Green. 24 17 7-0 

Sid. T. at Sp. (*'s R.A.) 2830 8 

Long, in time 4 13 i = 63 15' 15" E 

In this example, as the star was only 10 from the meridian, and the ship had receded 
from the star, o' 30" less altitude was set to the sextant for the second observation. 

There is no more work here than with the sun, as there is no equation of time to 
apply, and it is even easier to correct the sidereal time than the equation of time. 

The writer's usual morning double altitude was taken 3 m. before this first sight, by 
Saturn and Sirius, both east of meridian, the resultant giving longitude, when brought 
up to the same time, within i' of the equal-altitude longitude. He has taken several 
with equally good results, though in this case it was probably accidental that so near 
an agreement with the other observations was obtained, as better results might have 
been expected with a longer interval of time, when the star would have been nearer 
the prime vertical ; daylight, however, prevented this. 

It is best to choose stars with declination nearly the same as latitude, or else of the 
same name and the declination less than the latitude. If the declination is greater than 
the latitude, as in the last example, it does not come to the prime vertical at all ; neither 
does it if the declination and latitude are of contrary names. With latitude and de- 
clination of same name, when the numbers corresponding to the hour-angles in Tables A 
and B nearly agree is always a good time. For instance, in latitude 46 N., at hour- 
angle oh. 20 m., with * Capella, the numbers in Tables A and B exactly agree, both 
being n-8' ; Capella, therefore, with that latitude and hour-angle would be exactly on 
the prime vertical. 

The following example (on p. 128) will show how a star may sometimes be 
observed almost on the prime vertical to within 2 or 3 minutes of its meridian passage, 
or at any time within 2 or 3 hours of its transit. 



* The actual observations for this and the following example were taken in 1885, but for the sake of 
uniformity are here worked for the year 1898. 



128 

EXAMPLE 4. Longitude by Equal Altitudes of a Star nearly East or West. 

5. Colombo towards Aden. On i3th October, at 6h. 2401. and 6h. 3401. p.m. 
(ship time). Observed equal altitudes of # Altair at 2h. i6m. 553. and ah. 28m. 243. 
by a chronometer which was fast of G.M.T. 39m. 45. Star's azimuth at ist obns., 
S. 80 E. Lat. by meridian altitude, 8 46' N. Run in interval, N. 80 W., distance 
2 m. 



ist chron. time 
2nd chron. time 



Chron. time of transit 
Chron. error 

M.T.G. of transit 
Sid. T. (G. noon) 
Accl. for ih. 43 Jm. 

Sid. T. at Green. 

Sid. T. at Sp. (#'s R.A.) 

Long, in time 



H. M. s. 
2 16 55 

2 28 24 

2)4 45 19 

2 22 39-5 

- 39 4 

I 43 35'5 
13 28 16-3 
+ 17 

15 12 8'8 
19 45 SI'S 



4 33 42-8 = long. 68 25' 42" E 



Equal altitudes of this star were taken in the twilight for three or four evenings 
running. A few miles change of ship's position N. or S. in this case would not have 
affected the longitude i'. 



The following example gives the position of ship, latitude by ex-meridian 
(with azimuth 45), and longitude from equal altitude observations. The problem 
is also plotted on the chart, and the same result obtained. 



POSITION OF SHIP BY SHORT EQUAL ALTITUDE OBSERVATIONS 

OF SUN. 

1898. On March 2Oth, about noon, approximate position of ship on Equator 
in longitude 75 E. Observed alt. of o's L.L. was 89 20' S.E. when a chrono- 
meter indicated M.T.G. 19 d. 1.9 h. 6 m. 9 s., and again (p.m.) the observed alt. of O 's 
L.L. was 89 20' S.W. when chronometer indicated M.T.G. 19 d. 19 h. 9 m. is. 



Course and distance run between the observations west 
Required position of the ship at apparent noon. 



Height of eye 40 ft. 



M.T.G. (a.m.) 
M.T.G. (p.m.) 



D. H. M. 

19 19 6 
19 9 



Middle time by Chron. 
Eq. of time 

A.T.G. 
A.T.Sp. 

Long, in time 



2) 38 15 10 

19 7 35 
- 7 35 



o o 
o o 



500 



Longitude noon 75 o o E 
Long, at 2nd Obn 74 59 45 E 



M. s. 

Interval 2 52 
RunW - 2 

2)2 50 
H. A. i 25 



Decl. 



i 57 S 
4 57 S 



Cor. decl. o 6548 



Obsd. alt. 89 20 
Cor. (p. 87) + 10 

True alt. 89 30 



hrs. 
Hr. var. 59-3 x 5 



296-5 
4 56-5 



M. s. Var. 
Eq. T. 7 31-4 s. hrs. 
Cor. + 37 75 x 5 



Cor. eq. T 7 35'i 375 



FOR REDUCTION. 



FOR AZIMUTH. 

M. s. 

H.A. i 25 Sin 7791 
Alt. 89 30' Sec 2-059 

Az. 45 6 Sin 9-850 



T. Alt. 
Redn 



Az. 45, Table C (p. 4o) 
gives in Lat.o A and B Cor. 
i-o' which gives (p. i4s) 
Redn at mi. 6'2' x r42 m. 
= Redn 8-8' 



M.Z.D. 
Decl. 



Lat. 



89 30-0 S 
+ 8-8 



Mer. Alt. 89 38-8 S 
90 o-o 



21 '2 N 

o 6-9 S 
o 14-3 N 



129 

The accompanying chartlet gives a good illustration of the " Sumner " prin- 
ciple in connection with this problem without any logarithmic calculations for 
H. A., azimuth, or reduction, and it confirms the above method of calculation. 

We are indebted for this method to the writer's old friend Captain T. S. 
Angus, Nautical Inspector for the P. and O. S. N. Company, one of the keenest and 
most enthusiastic navigators he ever met. The method is as follows, viz. : Observe 
an altitude while the azimuth is yet large, and as soon as the Z.D. is small enough 
to be conveniently measured on the chart with a pair of dividers. Plot the 
geographical position of the sun (lat. = decl., long. = G.A.T.), and from this 
position as centre sweep an arc with Z.D. as radius. This is a position-line. Wait 
until the azimuth has sufficiently changed to give a good cut, and repeat the 
operation, the intersection gives the position at once without any further calcu- 
lation. 

The following figures give all that is necessary for plotting on the chart. 

H. M. S. , H. M. S. 

ist obsn. A.T.G. 18 58 34 W or Lat. (decl.) o 6-9 S 2nd obsn. 19 i 26 W or 

Z.D. o 30 as radius 

5 i 26 E 4 58 34 E 



Long. 75 21 30 E Long. 74 38' 30" E 

Run west 30 W 

Long, at time of 2nd obsn. 75 21 o E Chart position at 2nd obsn. Lat. o 14-2' N, 
^^=^. Long. 74= 59' 45" E. 



REMARKS ON EX-MERIDIAN AND MERIDIAN ALTITUDES. 

Although we have at the present day quite a number of special very useful ex- 
meridian tables, apart from the standard navigational epitomes, we would here remind 
those who use Raper that there are tables in that epitome which make very short work 
of this problem when within the ordinary ex-meridian limits, and the limits of 35 of 
declination. When within the limits of latitude 35 these tables may also be used 
for stars of any declination up to 62 N. or S., by using the declination as latitude, 
and vice versa. The following examples will illustrate this : 

EXAMPLE i. In lat. by D.R. 10 N., T. alt. of # a Crucis 16 10', hour-angle of 
star i h. lorn. Required the reduction to meridian. 

H.A. ih. iom. 

Lat. 10 N. ) decl. 62 35' S. f Table 70 Log 9-978 
as decl. j as lat. 1 i h. 10 m. Sin2 8-364 

Reduction i 15 34 . Sine 8-342 

True reduction i 15 19 

EXAMPLE 2. In lat. by D.R. 23 30' S., T. alt. of * a Crucis 50 53', hour-angle 
oh. iom. Required the reduction to meridian. 

H.A. oh. iom. 

Lat. 23 30' S. ) decl. 62 35' S. J Table 70 Log. 0-127 
as decl. I as lat. ( oh. iom. Sin2 6*678 

Reduction 2' 12" .... Sine 6-805 

In the first example the error from the calculated reduction by Raper's table 
only amounted to 15" with no error in the second, although the first example was 
outside the limits of the ex-meridian tables of Brent, Walter, and Williams, which 
tables until lately were considered to have exceptional limits, especially on account 
of comprising declination limits up to 70. 

The tables, however, at the end of this book are available for any latitude, or 
declination from Pole to Pole, and the time-limits of the first example might have 
been extended for another 50 min. without making more than about \' of error 
in the reduction. See limits on pp. 144 and 152.* Larger ex-meridian tables by 
the author, which are published in another volume, give still more extensive limits, 
sometimes as much as 3 hours from the meridian (and in a new edition of the work 
now in the Press) when the azimuth is sometimes over 70 from the meridian. 

* Tables of Calculated Hour-angles and Altitude Azimuth Tables (30 N. to 30 S.), Ex-meridian 
Tables (70 N. to 70 S.), and Calculated Reduction and Azimuths of 30 Bright Stars (64 N. to 
60 S.), by H. S. Blackburne. Second Edition. Price los. 6d. Published in United Kingdom by Thos. 
Ainsley, James Brown and Son, and J. D. Potter. 



130 

In this work the actual reductions and azimuths are taken out at sight for 30 of the 
brightest stars for limits far exceeding that of any other reduction tables, and as 
the reductions and azimuths have been calculated for the actual declination of the 
stars a minimum of interpolation is required in the use of the table. It would be 
impossible to make position-finding from two stars simpler than by the aid of these 
tables. An example is given on p. 128 of this work with an altitude of 89 J and 
azimuth of 45. In this example the hour-angle was accurately determined by 
equal altitudes close to, the meridian, otherwise this latitude by ex-meridian would 
only be of value as giving a latitude on the meridian of the D.R. longitude, and 
the position-line or circle of altitude at right angles to the bearing of the object, 
to be used in conjunction with another observation. Taken as a single observation 
4 sec. of error in the time would make i' of error in the latitude. (See Table M, 
pp. 156 and 157.) 

EXTENSION OF LIMITS IN USE OF TABLES No. i AND No. 2. 

A very considerable extension of the ex-meridian limits of Tables No. i and 
No. 2 in this work can also be obtained by transposing latitude and declination as 
shown in example on p. 163. For instance, in Table i, in latitude 25 and declina- 
tion 50, contrary names, the limits of time within which a correct reduction can 
be obtained by the table is 150 m., but with latitude 50 and declination 25 it is 
only 49 m. Caution. It must, however, be remembered that you cannot get the 
correct azimuth or position-line by transposing latitude and declination, so that 
if latitude and declination are transposed for the reduction a further determination 
of the A and B correction will be required to find the position-line. 

VALUE OF HIGH DECLINATION STARS FOR EX-MERIDIANS. 

Stars with high declinations are especially valuable for ex-meridian observations, 
and in high latitudes it is best to choose circumpolar stars, near the meridian below 
the Pole, as these stars change very slowly both in altitude and azimuth, and con- 
sequently errors in time only produce small errors in the resulting latitude. The 
amount of error due to 4 sec. of time is seen at a glance from Table M, pp. 156 and 
157. It was the recognition of the great value of these stars for both latitude and 
azimuth that induced the writer to calculate the actual true reduction and azimuth 
for twenty of the brightest circumpolar stars up to 2 to 3 hours from the meridian 
at the inferior transit. These tables make it almost as easy to determine the latitude 
by ex-meridian as by the meridian altitude when within the limits of the table, 
and also to set the sextant to the approximate altitude, which is a great advantage 
when taking twilight stars. The writer has lately calculated the reduction and 
azimuth in the same way for thirty of the brightest stars when near the meridian 
at the superior transit. High-declination stars are also preferable for observations 
of the meridian altitude, as a few minutes will then generally elapse without 
any appreciable change of altitude, both before and after meridian passage ; 
and it is a good plan to take several observations say, 5 m. before to 5m. 
after meridian passage unclamping the index each time, and to take the mean of 
these observations for meridian altitude. This plan is far preferable with stellar 
observations for latitude (except when altitude is very high) to that which is so 
often adopted of watching for the star beginning to fall. 

It is necessary to caution against this prevailing plan (in these days of rapid steam 
navigation) even with the sun, as by so doing the observation is sometimes taken lorn, 
or more after noon, and at others a few minutes before noon. This was brought pro- 
minently to the writer's notice many years ago, when second officer of a new mail- 
steamer. He made it a practice always to correct his watch and the ship clock before 
noon by comparison with chronometer and longitude applied. On one occasion 
when proceeding due south off Cape Finisterre, in a winter month, the captain and a 
couple of officers were observing for the meridian altitude. The writer reported that it 
was noon when his watch came round to the hour, but the captain said he did not make 
it so, and the sun was still rising ; we all therefore remained aft by compulsion until 
the captain made the sun to dip, at about lom. after noon, and the writer was wrongly 
and thoughtlessly blamed for the clock being in error. In this particular case the ship 
was steaming directly towards the sun at about 14 knots an hour, and by this change of 
position, had the sun been stationary, the altitude would have increased 14" in i m. 
.of time, or 70" in 5m. of time, and had the ship been stationary the sun would have 
only dipped o' 36" in that time ; therefore the altitude would have increased to observer 
o' 34". The sun's change of declination in lom. would only amount to 2", and is not 
therefore taken into account. 






131 

If the clock had then been put back, and bearings of the land had been obtained, 
the supposed meridian altitude would have given a latitude 2-4' N. of that 
by bearings ; or if the time had been taken by chronometer, and the observation 
worked out as an ex-meridian, it would be found that a correction of 2-4' was 
required to be added to the altitude. Should the observation be taken of a 
high-declination star, such as a Crucis, anywhere in the tropics, either north or 
south of the Equator, the natural fall of altitude in lorn, would be less than 2^' 
if latitude and declination were of same name, and barely i' with latitude and 
declination of contrary name. When the meridian altitude of the moon is observed 
for latitude the moon's change of declination must also be remembered, which is 
very rapid when near the Equator, varying in different years from a little over 9' 
to a little over 1 8' an hour. 

Mr. C. Westland has drawn the writer's attention to a method of finding the hour- 
angle of maximum altitude by the help of the A & B Tables, as follows : 

c .,. *5 f (Formula of Ex-meridian 

Assume reduction at i m. from meridian = t Table No 2 ) 

Then H.A. of maximum altitude is given in minutes of time by and since 

i m. of time is equal to 15' of arc it follows that the numerator of this fraction is the 
required H.A. expressed in arc. 

Rule. Express the difference in motion of lat. decl. (that is K) in minutes of arc 
per minutes of time, and multiply it by A + B for i m. To reduce to time subtract 
one third and move decimal point one place to left. 

Example. Using data above, and disregarding change of decl. (as it only amounts 
to 0-2" in im. of time), K = 14" = 0-233'. 

Lat. 43 N A 2137 S 
Decl. 23 S B 97-3 S 

C 311-0 x K 0-233 = 72'46 = 4-83. = 4m. 505. Required H.A. of maximum altitude. 
^^^ Subt. | 24-15 

48-31 

This method is considerably shorter and easier to remember than the methods 
usually given in navigational books. 



A FEW NAVIGATIONAL NOTES AND CAUTIONS. 



EXCEPTIONAL EXCESSIVE REFRACTION NEAR THE HORIZON.* 

It has often been pointed out in text-books of navigation and elsewhere that alti- 
tudes observed at sea are subject to error when peculiar atmospheric conditions operate 
to produce an extraordinary deflection of the ray of light from the horizon, and thus to 
make the actual angle of dip vary from its tabulated value. It is believed that attention 
can not be too frequently directed to this important subject, for the reason that there are 
undoubtedly many navigators who do not realize the magnitude of the error that may 
be involved : some have the impression that this error is such as to throw the results 
out by no more than a mile or so, and hence may be neglected for all practical purposes ; 
others, while knowing that in the Red Sea and other special localities the error is to be 
guarded against, do not consider that it need ordinarily be feared by the navigator. It 
can be demonstrated that this error may attain a value so great as to jeopardize a vessel, 
even if a very large margin be allowed for inaccuracy of the sights, and that the condi- 
tions under which it is produced are such that it may occur in any region of the ocean. 

It has been seen that the conditions necessary to produce extraordinary deflection? 
of the rays require that the atmosphere shall arrange itself in a series of horizontal 
strata of uniformly varying density. It follows, therefore, that the mere difference in 
temperature between air and water is not sufficient in itself to produce the error, and 
that any cause that interferes with the formation of strata will prevent the occurrence 
of the deflection. As wind, by keeping the air in motion, renders the conditions un- 
favourable for the existence of layers of unequal density, it follows that a light breeze will, 

* Extract from a publication issued by the Bureau of Equipment, Department of the Navy, Washington 
D.C. ; by Lieutenant G. W. Logan, U.S. Navy. 



132 

in general, greatly reduce the error, and that a strong one will effectually prevent it. 
Hence it is that the maximum bending of rays is to be expected in calm weather. It 
seems probable that the stratification is more likely to be disturbed when the air is 
colder than the sea than in the opposite condition, since the heavier particles are then 
above the lighter, and the atmosphere is in a state of unstable equilibrium that may be 
easily disturbed. 

Both theory and experience show that the higher the eye of the observer is placed 
above sea-level the smaller are the deflections from the causes under consideration. 
It is therefore well, especially when there is reason to suspect the conditions that pro- 
duce abnormal deflections, to observe altitudes from the highest available position. 

One of the most dangerous features of this error is that there is no satisfactory 
method of arriving at a correct estimate of its amount. If the conditions with which 
it is necessary to deal were fixed in their nature, such, for example, as the mean atmo- 
spheric conditions for which the ordinary dip-table is computed, it would be a simple 
matter to arrive, either by theory or experiment, at the amount of the deflection. But 
the elements of the problem can not, in their nature, be known. For instance, the 
conditions of temperature and wind at a distance of several miles from the observer, 
which can not be determined at the ship, have an important bearing on the solution ; 
so also with the amount of moisture in the air, which is doubtless a material factor. 
The navigator may, however, recognize the existence of the disturbing conditions and 
the probable direction in which the disturbance will affect the results of his observa- 
tions, and with this knowledge he must make ample allowance for possible errors. 

From a very large number of recorded instances of abnormal deflections of the 
rays of light from the horizon, due to inequality of temperature between sea and air, a 
few will be chosen to illustrate the possible magnitude of this error. 

It is related that on one of Captain Cook's voyages the meridian altitude of the sun 
was being taken when a light snow-squall came on. The horizon and sun remaining 
visible, the altitude shown by the sextant had almost instantly to be altered 32' to 
maintain contact, the horizon having appeared to fall by that amount when the air sur- 
rounding the observers was cooled by the snow-squall. At the same time a distant 
mountain-peak, which before had stood well above the horizon, almost disappeared 
from view. Both of these effects vanished with the passing of the squall, the measured 
altitude resuming its former value and the peak rising again above the horizon, Even 
if we are inclined to doubt the instruments of those times, and therefore the exactness 
of the observed difference, this account is of interest in showing at how early a day the 
presence of this error was recognized in navigation. 

According to Raper, Mr. Fisher observed in the Arctic regions a variation of 18' 
in the place of the horizon. 

The late Captain Lecky, in his " Wrinkles," states that on a clear day in mid- 
winter, off the coast of Long Island, five observers at noon closely agreed upon an 
altitude which gave a certain latitude ; in less than two hours afterwards the land was 
sighted, and the latitude brought forward from the meridian altitude was found to be 
14' in error. 

Lieutenant Koss and Ensign Thun-Hohenstein, of the Austrian Navy, while con- 
ducting observations near Pola for finding the variation in the dip of the horizon, 
observed on a quiet day a rise of the apparent horizon above its computed position of 
8' 47" at a height of 50 ft., and of 9' 23" at a height of 33 ft. above water. 

Of the numerous instances that might be cited of extraordinary errors in the results 
given by astronomical sights in the Red Sea (so extraordinary as to have given rise to 
an erroneous belief as to the currents existing in that body of water), it may be men- 
tioned briefly that Lieutenant Marshall, U.S. Navy, of the U.S.S. "Detroit," found 
errors of position from 12' to 18' arising from sights of the sun ; Captain Nedden, of 
the s.s. " Madeline," found the latitude by observation to differ 10 miles from the cor- 
rect one, and images of islands to be greatly distorted ; and Captain Lecky discovered 
the positions of certain islands to be apparently 7 to 8 miles in error in one direction 
from morning sights, and a similar amount in error in the opposite direction from 
afternoon sights. 

A similar instance of error in the region of the Gulf Stream was reported by Lieu- 
tenant-Commander W. L. Rodgers, U.S. Navy, of the U.S.S. " Lancaster," two lines 
of position from the sun intersecting at about 7 miles to the south-east of the ship's true 
position, and two from stars intersecting at a like distance in the opposite direction, the 
direction of the error in each case according with that which was to be expected from 
the observed differences in temperature of air and water. 

As a result of what has been set forth, the following brief summary may be given 
for the guidance of navigators : 

(a.) The inaccuracy of tables showing the dip and the visibility of objects should 
.always be suspected when there is a marked difference between the temperature of the 
air and that of the sea- water. 




133 

(b.) The errors will be largest in calm weather and when the eye is not far elevated 
above the sea, and will decrease as the wind increases and the eye is raised. 

(c.) When the air is warmer than the water, the visible horizon is raised above its 
normal position ; the altitude corrected by the ordinary dip-table will be too small, and 
the resulting Sumner line will be farther from the observed body than the true line. 
An object will be sighted from a greater distance than usual. 

(d.) When the water is warmer than the air, the visible horizon is lowered below 
its normal position ; the altitude corrected by the ordinary dip-table will be too large, 
and the resulting Sumner line will be nearer the observed body than the true line. An 
object will be sighted from a less distance than usual. 

"A few years before the time of writing this a very well authenticated 
case of undoubted excessive refraction was brought to the notice of the writer by an old 
pupil (Captain W. H. Sweny), then commanding the P. and O. s.s. " Mooltan." At 
about 6 p.m. on April nth, 1910, he took observations of four different stars for a posi- 
tion viz., Procyon (ex-meridian) to northward, Rigel to north-westward, Canopus to 
south-westward, and /3 Centauri to south-eastward, to cross with one another. The 
chief officer took an ex-meridian of Pollux to northward, and Rigel and /3 Centauri 
for a cross. Shortly afterwards the fourth officer took Procyon, Canopus, /3 Cen- 
tauri, and Jupiter to eastward. Captain Sweny first sent the writer his own 
observations, asking him to work them out and let him know what he made 
the resulting position. This was done, and when the captain afterwards sent the 
results of his work both positions were in agreement and evidently not more than 
about i' in error in either latitude or longitude. The captain also sent the worked- 
out observations of the other two officers, and from all these observations the writer 
was able to deduce fairly accurate separate positions, and it was evident from these 
observations that refraction was excessive all round the horizon, but greatest to the 
northward, where it was about ii - o', and in other parts of the horizon averaging 
about 6f ', the altitudes being smaller by these amounts than they should have been by 
allowing the usual tabular corrections. The height of eye when these observations 
were taken was 50 ft. If the captain had been satisfied with the ex-meridian observa- 
tions of Procyon and Pollux, and the longitude of Centauri, he would have been n' 
or 12' out in the latitude and 33' out in the longitude. By using the observations 
intelligently he was practically correct in his position, and made Rottnest Light nearly 
ahead at 2 a.m. His position at the time was about 30 4' S. and 113 47' E. 

The above related experiences, though undoubtedly very exceptional, should tend to 
warn navigators not to trust too implicitly even in daylight to observations taken on 
one side only of the meridian, or prime vertical ; for though such excessive refraction is 
very rare, and may not be experienced in the lifetime of a frequent observer, it is 
probable that such amounts as 2' difference from the tabulated value of refraction 
is not uncommon. 

EFFECT OF ALTITUDE ERRORS. 

With a.m. sights too great an altitude will place a ship to eastward of true posi- 
tion, and vice versa with p.m. sights and too small an altitude. The amount of error in 
longitude or time due to i' error of altitude is shown in Table D. 

OBSERVATIONS IN ARTIFICIAL HORIZON. 

In correcting the altitude taken in artificial horizon, first apply index error, thec 
halve the altitude after which apply the other corrections viz., refraction, parallax, 
and semidiameter. 

When the lower limb is taken with a.m. sights the suns appear to be separating, 
and when the upper limb is taken the suns appear to be closing in on one another. 
Vice versa with p.m. sights. 

NUMBER OF FIGURES TO USE WITH LOGARITHMS. 

Using more than four figures of logarithms in working any of the sailings is gene- 
rally a waste of figures ; as also in working an altitude or time azimuth or the time when 
hour-angle is less than 2 hours. 

In Bowditch's "American Practical Navigator" not more than five figures are 
given in any of the tables, and the work is thereby much facilitated. 

CORRECTIONS OF SUN'S DECLINATION AND EQUATION OF TIME. 

For ordinary sea practice it is generally useless precision when correcting the sun's 
declination to take out the hourly variation to decimals of a second ; also, one place of 
decimal is amply sufficient when correcting the equation of time. 



134 

CORRECTION OF A PLANET'S R.A. AND DECL. 

The R.A. and decl. of a planet may often be quickly corrected by the aid of the 
traverse-table used as a proportional table. The following example will illustrate this : 

1898. 3oth August; M. T. G. gh. 36m. Required the corrections for R.A. and decl. 
Daily change of R.A. was 236-3 s., and of decl. 28-8'. 

To find correction for R.A, due to Q'6h. from noon: Add a cipher to 24 h., then 
with 240 in dist. column look out the nearest number abreast it in either the dep. or 
d. lat. column. This will be found at 10 in d. lat. column viz., 236-4. Having added 
a cipher to 24 h. the decimal point in 9-6 h. must be removed one figure to the right ; 
then look out the number in d. lat. column against 96 in dist. column and the correction 
94-5 s. will be found. 

To find correction for decl. due to 9-6 h. from noon : 28-8' is the change in 24 h. 
At 33; in the traverse-table we find 239-9 in d. lat. column against 286 in dist. column, 
and again 96-4 in d. lat. against 115 in dist. .*. 11-5' will be the correction (nearly). 

NOTES ON MERCATOR AND MIDDLE-LATITUDE SAILINGS. 

Mercator's sailing should be used generally when the course is between i and 70, 
especially with long distances and in high latitudes. With a large course, and using 
either Raper or Norie, the distance may sometimes be considerably in error owing to 
the meridional parts not being given to decimals. The following examples will illus- 
trate this : 

Find the true course and distance from lat. 5 28' N., long. 85 30' E., to 
lat. 5 34' N., long. 91 o' E. 

BY MERCATOR'S SAILING (RAPER'S TABLES). 



Lat. 5 28 N Mer. pts. 328 Long. 85 30 E 
Lat. 5 39 N Mer. pts. 340 Long. 91 o E 


Log 
Log 

Tan 


12-5185 
1-0792 


D. lat. Log 
Sec 
Log 
Distance 


1-0414 
I-4396 


D. lat. ii N M. d. lat. 12 5 30 E 


60 


D. long. 330' 
M. d. lat. 12' 

Course N. 87 55' E. 


"'4393 




2-4810 


302*7 mile? 



BY INMAN'S TABLES. 

5 28 N Mer. pts. 328*50 D. long. 330' Log 12-5185 

5 39 N Mer. pts. 339-55 M. d. lat. 11-05' Log 1-0434 D. lat. n' Log 1*0414 

D.lat. ii N M. d. lat. 11-05 Course N. 88 5' Tan 11-4751 SecofCo. i'4753 



Distance 328-6 miles Log 2-5167 
Raper 302-7 s=^ 



Difference 25-9 miles 

BY MIDDLE-LATITUDE SAILING. 
D 

Lat. 5 39 N 



Lat. " 5 28 N D. long. 330' Log 2-5185 

Mid. lat. 5 33i' Cos 9-9980 



Course 88 5' Sec 1-4753 



Mid. L. 5 33! Dep. 328-5 Log 12-5165 D.lat. ii' Log 1-0414 

D. lat. ii' 



Log 1-0414 



Course 88 5' Tan 11-4751 



Dist. 328-6 miles Log 2*5167 



To take out the distance accurately for a large course, as between 85 and 90, the 
log. of secant should be taken out to seconds ; this may be practically done by bearing 
in mind that the secant and tangent differences here are almost the same. Thus in the 
last example the difference between the sec. and tan. in the fourth figure is about 2 ; 
then add 2 to the log. tan. of course. 

When the course is large the distance is very readily found from the traverse-table 
by a comparison of the dep. with the dist. column. For instance, with an 88 course, 
distance 329 is 0*2 greater than the departure; with an 87 course, distance 329 is 0-5 
greater than the departure. In the same way, when the course is within 3 or 4 of the 
meridian, the distance will be nearly the same, but a trifle greater than the d. lat. 






135 



SIMPLE METHODS OF FINDING THE SHIP'S DISTANCE FROM A 
POINT BY TWO BEARINGS AND THE RUN IN INTERVAL 
BETWEEN THEM. 

As so many strandings have occurred on the New Zealand coast owing to the 
neglect to take or make use of bearings, it has been thought advisable to give the 
following simple methods for approximately determining the ship's distance from a single 
point or light when cross-bearings are not obtainable. The methods here given have 
the advantage of being determined quickly, with a minimum of calculation, without 
leaving the deck or having to plot the bearings on a chart. Figure 3 and Table H were 
first published in the writer's first edition of " A and B Tables," &c., and their value 
has since been further impressed on navigators by the late Captain Lecky in the latest 
editions of his famous " Wrinkles." The writer has also been pleased to notice that 
some of the local steamers now have a brass plate on the bridge marked somewhat 
after the style of Figure 3. 

PROBLEM i. To find the Distance from a Point when the Angle on Bow is 

doubled. 

Whenever the angle between the course and object is doubled, the distance run 
in the interval is the distance off at second bearing. The well-known four-point 
bearing illustrates this, and, as the second bearing then gives the distance off abeam, 
it is most frequently used ; but it is often very useful to be able to know the dis- 
tance off at an earlier period, as illustrated by Fig. i. 




Example. A ship making 10 miles an hour on a S.E. course by compass sighted 
Kaipara light, bearing E.S.E. ; after continuing to make good the same course 
and speed for 57 m. the light bore E. Required the distance from the light when 
second bearing was taken. 

First bearing E.S.E. 2 points on bow; second bearing E. 4 points on bow; 
angle doubled : the distance run in interval between bearings will be the distance 
off at last bearing. Interval 57m. = $$ or 0-95 of an hour x 10 gives run in interval, 
9-5 m. the distance off. 

It is apparent from the figure that if this course is continued the ship will 
probably run foul of the North Spit. (See Fig, i.) 

Problem 2 will illustrate how by the aid of the traverse-table the course may 
quickly be set to pass a safe distance off. 



136 

PROBLEM 2. From a known Distance from Object, to set Course to pass any required 

Distance from it. 

Rule. Enter the traverse-table with the distance required to pass off in the 
dep. column and the present distance off in dist. column. The course heading 
this will be the angle to bring the object on the bow. 

Example as shown in Fig. 2. Ship steering S. 45 E. by compass, Kaipara 
light bore E. distant 9-5 m. Set the course to pass 8 m. off the light. Enter the 
traverse-table with distance 9*5 in dist. column, and turn over until the nearest 
to 8'o is found in dep. column. This is found at 57. Bring the lighthouse 57 
on bow, or course by compass S. 33 E 9*5 in dist. column gives 7*97 in dep., and 
5*17 in D. lat. column, the distance to run. Fig. 2 illustrates this 




The advantage of knowing the distance that a ship will pass off a point on a given 
course, in good time before coming up to it, struck the writer many years ago when he 
was quite a junior officer, and he then made out the figure given below, which has 
often been used since. 

The distance run in the interval between any two of the following bearings will 
give the distance that the ship will pass off the object if the same course is continued 
and made good. 



PROBLEM 3. To find the Distance a Ship will pass off an Object when abeam by the 
Distance run in Interval between certain Bearings as given below. 

Fig. 3. 




137 



Between 22 C 

'. 2 5 C 
265! 

'I 32 C 

- 37 

, 45 

45 



and 



. 45 L 

. 59< 

90 

, 63l c 



The distance run will be 
the distance the ship will 
pass off 



the distance run will be half 



the distance the ship will pass off. 



The numbers under base of figure represent the length of the base of the right- 
angled triangle proportionate to the perpendicular of 10. Thus, should the ship be 
passing 10 miles off an object, and the object be 22 on bow, ship will be 24-8 miles 
from the beam bearing. 

The traverse-table gives the three sides of right-angled triangles for every 
degree of angle subtending the base or perpendicular. If, therefore, we know the 
angle on bow and the perpendicular i.e., the distance the ship will pass off the 
point when abeam the other two sides of the triangle viz., the distance off at 
the time, and the distance to run to beam bearing are seen at a glance from the 
table. 

Say angle on bow is 32, and previous bearings give distance to pass off 10 m. 
Open traverse-table at 32 and against 10 in dep. column, we have i8'g in dist. 
column as the distance off, and 16-0 in the D. lat. column as the distance to run 
to beam bearing. 

Example. A ship steering north observes a light bearing N. 32 E. ; after running 
on same course for 6-0 miles the light bears N. 59 E. Required the distance the ship 
will pass off the light if she continues on the same course, and the distance from the 
light at time of second bearing. Answer : Distance run in interval (6-0 miles) will be 
the distance the ship will pass off the light. Then, opening the traverse- table with 59 
as course, and 6 in dep. column, we find 7 in dist. column as the distance the ship will 
be from object at that time. 

As a ship changes the bearing of an object much more rapidly when nearing the 
beam bearing than at any other time, the distance that a ship passes off a point will be 
better determined by the run in interval between the two bearings of 63^ on bow and 
63 from stern or, in other words, when it is 26 from the beam bearing before and 
abaft than at any other time. 

It sometimes happens that a light or point is not sighted till after the ship has 
passed the four-point bearing. In such case Table H will be found useful, and might 
be copied out and put inside the wheel-house for ready reference. 



PROBLEM 4 (by Table H). To find the Distance from an Object when abeam by the 
Distance run between Beam Bearing and any other Bearing before or abaft the Beam. 



Table H. 






o 


o 


o 


o 


35 '7 


45 - oo 


55 '43 


65 2-14 


75 373 


36 73 


46 -04 


56 -48 


66 2-25 


76 4'oi 


37 '75 


47 - 7 


57 '54 


67 2-36 


77 4'33 


38 -78 


48 -ii 


58 -60 


68 2-48 


78 47 


39 '8i 


49 '15 


59 '66 


69 2-61 


79 5-I4 


40 -84 


50 -19 


60 -73 


70 2-75 


80 5-67 


41 "87 


51 -23 


61 -80 


71 2-90 


81 6-31 


42 -90 


52 -28 


62 -88 


72 3'o8 


82 7-12 


43 '93 


53 '33 


63 1-96 


73 3'27 


83 8-14 


44 '97 


54 1-38 


64 2-05 


74 3'49 


84 9'5i 



138 

Rule. Enter the table above with the number of degrees that the object is on the 
bow, and take out the factor given in the table abreast it. This factor multiplied by 
the run in the interval between the bearing on the bow and the 
4. bearing of the object when abeam will give the distance off when 




Example. A lighthouse is observed 70 on bow, ship's speed 
iom., and interval in time to beam bearing 48min. 

48min. = o - 8 of an hour x iom. = 8m. for the run in the 
interval. 

Against 70 in the table is 2-75, which x 8m. gives 22 m., the 
distance off when abeam ; or by traverse-table, enter with 70, and 
with distance run 8m. in D. lat. column, gives distance off in 
dep. column = 22 m., and 23-4 m. the distance off when first bearing 
was taken. 



CHART METHODS. 

PROBLEM i. To find the Distance from an Object by Two Bearings, and the Run in 

Interval between them. 

Rule. Lay off the first bearing and the ship's course, then lay off the last 
bearing, and measure off the distance run on the course since the first one was 
taken ; through this distance draw a line parallel to the first bearing : the point 
of intersection between this line and the second bearing should be the ship's 
position. 

Example (see Fig. 5). A ship steering from A towards B on a N. 20 E. course 
sights a point bearing N. 65 E. ; after running on this course for 18*5 m. the point 
bears S. 70 E. Required the distance off at second bearing by plotting on the 
chart. 

Lay off the course N. 20 E., also the bearing of P. N. 65 E. ; then measure 
18-5 m. on the line of course from this bearing, and make a mark ; through this 
mark draw a line parallel to the bearing N. 65 E. ; then the intersection of this 
line with the second bearing will be the ship's position, which gives 18*5 m. as the 
distance off. 



PROBLEM 2. To find the Distance from an Object by Two Bearings of Differ en 
Objects with Run in Interval between the Two Bearings. 

This problem is exactly the same in principle as the " Sumner " with two sun 
observations, and the writer when at sea often found it of great practical use, though 
he never found other navigators make use of the method (except after he had drawn 
their attention to it), nor is the method presented, so far as he is aware, in other 
nautical works. It is now given occasionally in New Zealand in the examination 
of masters and mates in the chart-examination problems. 

Rule. The rule for problem 2 will be exactly the same as for problem i. 

Example (see Fig. 6). A ship steering from C towards D on a N. 45 E 
course sights a point N. bearing S. 15 E. ; after running on this course for 
15-6 m. point R is sighted bearing N. 85 E. Required the distance from R at 
second bearing. 

Lay off the course N. 45 E. from C to D, also the bearing of N. S. 15 E. ; 
then measure 15-6 m. on the line of course from this bearing, and make a mark ; 
through this mark draw a line parallel to the bearing S. 15 E. ; then the inter- 
section of this line with the second bearing will be the ship's position viz., S. 85 
W. 17*2 m. from point R. 

This problem may often be used with advantage at night-time with two lights 
when one light is sighted shortly after the other one has been lost, or where the 
simultaneous bearing of two lights or two points makes too large an angle for a good 
fix. It will also be found useful in foggy weather in close navigation, where one 
near point after another may be just seen for a few minutes and then obscured 






139 

again. The bearing of these points in combination (the first bearing having been 
moved forward for the run in interval) will then generally give a good fix. 

The distances in these plottings have been taken from the diagonal scale below 
the figures ; the opportunity having been taken to draw attention to this handy 
useful scale, which any one can easily make for himself. 




:-.: . ^ \ ' ^ \ \ :. \ \ j Diagonal Scale /'/'/ ' . S' _ : 


i * i .] "" 


', 


- 'jt J 


:: 


^TT 








i 


















: 2r 


-f- 


s 








i 
















: 


!- n 


"rT 


g 


























: 


;. ' 2 ffi 


si 

-1 1 


1 


























-\ 


.!~~8 6 4 Z 





o 


^\ ' 


3 


4 


5 







EXPLANATION OF THE DIAGONAL SCALE AND PROTRACTOR. 

In the diagonal scale, the shorter lines dividing the length into equal portions 
(units) are crossed perpendicularly by 10 others extending the length of the scale. 
The end division, or unit, has its upper and lower edge subdivided into 10 equal 
parts, and diagonal lines are drawn from the beginning of one division to the end 
of the opposite one. This effects a further subdivision by 10, as an example will 
show. To take the No. 18*5 from this scale by the compasses : Set one foot at i, 
and the other at the 8th line on the lower edge of the subdivided unit ; this gives 
18. Now follow up the diagonal line at the 8 to the 5th line of the long parallel 
lines, and fixing the point there, extend the other point to meet the line which 
rises at i, crossing the breadth ; and the number is taken. 

io Azimuth. 



140 

The same process serves for tens and units as for units and tenths, and so 
on ; thus the No. 1-85 or 185 is taken as above. 

To lay oft or measure an angle by the marked divisions. Place the middle 
point of the scale or ruler (which is strongly marked) on the meridian line, and, 
keeping it there, incline the ruler to the required angle, which is shown by the gradu- 
ated scale of degrees coinciding with the upper part of the meridian line. Field's 
parallel ruler is marked in this way, and is very useful in laying off true bearings. 

Caution. The distance found by any of these methods from bearings with a run 
interval must only be considered as an approximation, as they depend on the course and 
distance run in interval having been made good. If, therefore, a current is known to 
exist, allowance must be made for it. 

Cross-bearings of two (or, better still, three) prominent points will give a more certain 
position, provided the error of compass is known, and the angles are neither too large 
nor too small for a good " fix," and the points are accurately laid down on the chart; 
but every careful man will have at least two strings to his bow, and the position as 
found by run and interval will be a good check against possible errors. I think every 
one will admit their liability to such mistakes as reading off the wrong bearing, or 
applying the variation the wrong way, &c., and for this reason it is therefore always 
better to take three cross-bearings, when such are available. 

Examples in the use of all these methods of finding the position of the ship by 
bearings, either with or without the chart, are given in the New Zealand examinations 
of either the home or foreign-going candidates for masters and mates. 

THE COMPASS AND PELORUS. 

Some owners do not seem to realize the value of having a proper compass, with a 
suitable position selected for it in the ship. Dozens of New Zealand ships would but 
for the Adjusters' reports be without any proper appliances for taking bearings, and 
many of the compasses are so closely surrounded by iron that no deviation card can be 
depended on. I would like here to point out the value in coastal navigation of having 
a Pelorus, which can be shifted to a stand made for it from one side of the bridge to 
the other, as is needed. The instrument is generally made of brass, being a dumb com- 
pass card without needles. It is a convenient plan to have the Pelorus set to the true 
geographical course, or else the magnetic course the ship is steering ; then any bearings 
taken by it will be true, or magnetic, as the case may be, and free from the trouble of 
applying the error or variation of the compass. It may also be set to zero, N. or S., 
and the angle on the bow will then be readily read off for greater convenience in finding 
the distance off points, as in the problems which have been here mentioned. 

Warning. Do not use the Pelorus for long-distance bearings, such as Mount 
Egmont, 50 miles off. 

LECKY'S DANGER-ANGLE TABLE. 

When mentioning up-to-date methods of finding the ship's position at sea, Lecky's 
spier did little book, " The Danger-angle and Off-shore Distance Tables," ought not 
to be passed over. The book is in two parts : The tables in Part I comprise heights 
from 50 ft. to i, 100 ft., and distances from a cable's length up to five miles; they can 
only be used in connection with objects lying on or within the bounding line of the 
observer's horizon ; for objects beyond the horizon Part II has been calculated. The 
tables in Part II comprise heights from 200 ft. to 18,000 ft., and distances from five 
miles up to 100 miles. They are intended to be used with objects lying beyond the 
horizon, and the observed altitude must be corrected after the index has been applied 
by subtracting the true depression corresponding to the height of the eye, and also 
one-twelfth of the roughly estimated distance from the mountain. Under the result 
as a corrected altitude, and abreast the height of the summit in the left-hand margin 
of the tables, will be found a very close approximation to the true distance. This 
distance, combined with a bearing of the mountain, fixes the ship's position with a 
minimum of labour. For an example, suppose the peak of Mount Egmont to be 
observed from the ship's deck 25 ft. above the water, bearing east magnetic, 

Altitude . . . . . . 2 32' o" 

25ft. dip (from table) .. 5 19 

Approximate distance . . . . 2 26 41 

One-twefth of approximate distance 2 30 



M?E gm oni ' V/o ft' 1 } Klve. distance off 



SUPPLEMENTARY 
EX-MERIDIAN TABLES 



142 



EXPLANATION OF TABLES. 



Ex-meridian Table No. 1. 

The factor under the heading of Reduction abreast the A and B Correction is the 
reduction at i min. from the meridian to apply to an altitude to reduce it to the 
meridian altitude. 



INSTRUCTIONS CONCERNING THE USE OF TABLE AND RULE FOR APPLICATION. 

Multiply the factor corresponding to the A and B correction under the heading of 
Reduction by the number of minutes and decimals in the hour-angle from the meridian, 
which then gives the correction to apply to the observed altitude to reduce it to the 
meridian altitude. Add this correction to the observation taken near the upper meridian 
passage, and subtract the correction when observation is taken near the meridian below 
the Pole. 

This reduction will not be more than ' in error when the hour-angle is less 
than that shown in the accompanying table immediately following, which shows the 
limits within which it is safe to use the table without appreciable error. 

The table gives the correct reduction at i m. from the meridian for any azimuth 
up to 45 from the meridian, or the equivalent A + B correction in latitude o, and 
has been rigorously calculated by seven figure logarithms from the following 
formulae : 

Cot. Z.D. = sin. azim. cot. H.A. i m. 

Tan. decl. = sin. H.A. i m. cot. azim. 

Cot. az. = A B correction. 

In latitude o decl. = M.Z.D. and Z.D. - M.Z.D. = reduction. 



TABLE SHOWING LIMITS OF REDUCTION TABLES No. i AND No. 2. 

These two tables show at a glance the hour-angles at which it is safe to use Re- 
duction Tables No. i and No. 2, so that with the correct time the reduction will not be in 
error more than '. It must, however, be borne in mind that the resulting latitude 
is the latitude corresponding to the meridian of longitude used in the deduction 
of the time. The A and B correction through Table C readily gives the azimuth, 
which subtracted from 90 gives the true line of position for a Mercator Chart ; 
or through Table C 2 it gives at once the position-line for use with a plane chart. 
This position-line must be laid down from the meridian of the D.R. longitude used 
in determining the time. 

When the H.A. is on, or four or five minutes less than the limit given in the 
table, 0-4' may be added to or subtracted from the reduction calculated by 
Ex-meridian Tables No. i and No. 2, according as the letter against the minutes is g 
or /. If the H.A. is more than 5 m. less than the limits in the table the reduction 
may be considered as correct, and in either case the resulting reduction would 
seldom be as much as J' in error. 

When the letter n is marked after the minutes in the table the resulting reduc- 
tion will seldom be as much as ' in error. When the altitude is over 75 both 
time and altitude should be used in the determination of the azimuth, and the 
A and B correction corresponding to this azimuth should be used in finding the 
reduction. See examples on pages 105, 128, 158, 160, &c. 



143 

Ex-meridian Table No. 2. 

The instructions and rules relating to this table are exactly the same as for 
Table No. i. 

Formula used in the calculation : 



Reduction for i min. 



2 [A + B]. 



NOTE. This table is entirely independent of Table No. i, which will generally 
give the best results and widest limit. Table No. 2 is given on account of the wide 
limits of reduction which it gives with high declinations and low latitudes ; and 
the same wide limits may be obtained when in high latitudes, and low declinations 
by transposing latitude for declination, and vice versa. A glance at the tables 
showing the limits of the two ex-meridian tables will at once show whether it is 
most advantageous to use No. i or No. 2 Ex-meridian Tables. (See example 
page 163.) 



Table M. 

SHOWING THE ERROR IN LATITUDE DUE TO AN ERROR OF 4 SECONDS IN TIME OR 

1' OF LONGITUDE. 

This table (pages 156 and 157) shows at a glance the error which would result 
in the latitude from any single observation out of the meridian for every 4 sec. of error 
in the time. 

When two observations are taken the factors given in this table facilitate the 
problem of finding the ship's position from two ex-meridian observations, or one 
chronometer observation, and an ex-meridian (see page 95). 

Formula used in the calculation: Lat. error = Tan. azim. cos. lat. 



144 



Table showing the Hour=angle Limits within which the Error of the 
calculated by Ex=meridian Table No. 1 will not exceed 05. 



Redu 



ction 



LATITUDE AND DECLINATION OF SAME NAM]:. 




DECLINATION. 


"rt 





2 4 


6 


K 


10 


15 20 


25 


30 


35 


40 


45 


50 


60 


70 





M. 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


O 




8n 


i6n 


2 4 W 


3 2n 


4 og 


4 2g 


44g 


4 6g 


4 8g 


5ig 


53g 


55g 


5 8 g 


63g 


7 Ig 


I 


4* 


4n 


I2n 


2on 


28n 


35g 


39g 


42g 


4 5g 


4 7g 


50g 


5ig 


55g' 


56g 


62g 


jig 


2 


8n 




8n 


i6n 


24 


n 


32 


36g 


4g 


43g 


46g 


48g 


5^ 


53g 


56g 


62 g 


7g 


3 


i2n 


4 n 


411 


1211 


2on 


28g 


35g 


38g 


4 2g 


46g 


48g 


4 9g 


52g 


56g 


62 g 


6gg 


4 


i6n 


8n 




8n 


i6n 


2 4 g 


34g 


35g 


4ig 


4 5g 


47^ 


4 8g 


50g 


55g 


62g 


68g 


5 


2on 


I2n 


4n 


4 w 


I2n 


2on 


3*g 


35g 


4 og 


44g 


4 6g 


4 8g 


5^ 


54g 


62 g 


68g 


6 


2 4 l 


1 61 


8n 




8n 


i6n 


3g 


35g 


39g 


43g 


4 6g 


4 8g 


5g 


53g 


6cg 




8 


241 


20l 


1 67 


8n 






8n 


29g 


34g 


37 g 


4 ig 


44g 


47^ 


48^ 




6cg 


66g 


10 




227 


1 7 l 


i 4 7 


81 




2on 


34g 


3 6g 


39g 


4 2 g 


44 


48g 


5^g 


57 g 


66g 


12 


261 


227 


207 




13' 


87 


127 


35g 


35g 


37 g 








5g 


57 g 


66g 


15 


27' 


25' 


227 


207 


i 7 7 


i 4 7 






4g 




39^ 


4 3g 


44 g 


4&g 


55g 


&5g 


20 


281 


2 7 7 


247 


23' 


2C 


/ 


igl 


nl 




1 67 


5ig 


39g 


42g 


4 2g 


46g 


53g 


6 3 g 


25 


3' 


287 


2 7 7 


267 


2i 


/ 


227 


I 7 l 


ioi 




13' 


2 9 7 


45^ 


43g 


46g 


5 T g 


6ig 


3 


3 2 ' 


3 o7 


29/ 


287 


261 


25' 


2l7 


1 61 


9' 




127 


2 7 7 


54g 


46g 


48g 


59 g 


35 


34' 


327 


31' 


3 o7 


287 


2 7 7 


2 4 7 


207 


15' 


o7 




13' 


267 


6og 






4 


35' 


34' 


33' 


327 


3i' 


3 o7 


2 7 7 


23' 


207 


167 


io7 




ill 


267 


5 c g 


56g 


45 




3 67 


34' 


34' 


32' 


327 




277 


2 4 7 


2l7 


1 67 


ic7 




13' 


65g 


54g 


5 


39' 


37' 


35' 


35' 


34' 


35' 


33' 


327 


287 


25' 


2l7 


1 67 


ill 




3 ol 


54g 


55 




4 o7 


38' 


37' 


37' 


37' 


367 | 3 4 7 


32' 


2 9 7 


257 


2l7 


i 7 7 


127 




59g 


IK) 


4 27 




4 o7 




35 


/ 4 o/ 


39' ' 39' 35' 


3 2 ' 


291 


267 


23' 


197 




48* 


INFERIOR TRANSIT. 


"NTOTTT 




DECLINATION. 


IN \J 1 Ji . 


J 


25 


30 


35 


40 


45 


50 55 


60 


65 


70 


g signifies that true re- 





M. 


M. 


M. 


M. 


M. 


M. M. 


M. 


M. 


M. 


duction is greater than 


2 5 




















gg_ 


tabular reduction. 


3 
















] 


OT.P 


C _~ 




as 














] 


3o7 


J6 
I 29 





I signifies that true re- 


O .J 

4.0 














8o7 ] 


oo7 


*-^b 

Sol 




duction is less than 


T 

45 












687 




867 ] 


id 


I 7 0g 


tabular reduction. 


5 


. . 








60 7 


6 5 ' 


7 o7 


80^ 


go I 


7 

1207 




55 


. 






567 


60 7 


6^7 


687 


74' 


861 


I0 5' 


n signifies that there is 


60 






54' 


57' 


59' 


627 


6 7 7 


7 o7 


7 8l 


Q27 


no error as great as 0.5' 
within limits of hour- 


65 

7 


53' 


4 87 
53' 


54' 
55' 


55' 

57' 


59' 

59' 


6o7 


6 5 7 
627 


697 
63' 


7 o 


8 4 7 
79' 


angle which give A + B 


75 


54' 


54' 






60 7 


6i7 


627 


667 


JOl 


78* 


greater than i 'ooo' 


80 




59' 


6o7 


627 


6 3 7 


6 4 7 


667 


687 


7 2l 


75' 




85 


667 


687 


697 


7 o7 


727 


727 | 74 7 


74' 






LATITUDE AND DECLINATION OF CONTRARY NAMES. 


. 


DECLINATION. 


3 





2 


4 


6 


8 


10 


15 20 


25 


30 


35 


40 


45 


50 


60 


70 


o 


M. 


M. 


M. 


M. 


M. 


M. 


M. M. 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


I 


4n 


I2W 


2on 


28n 


36^ 


4 2g 


4 5g 4 5g 


48 g 


50^ 


52g 


55g 


57 g 


59 


62g 


jig 


2 


8n 


i6n 


24n 


3 2n 


4 ( 


ni 


44g 


4 8g 


48g 


5g 




54S 


56g 


58g 


59^ 


63 


7 2g 


3 


I2n 


2cn 


28n 


3 67 


44' 


50% 


52g 


53f 


54g 


54g 


55 


57^ 


58g 


6og 


6 3 g 


73g 


4 


i6n 


2411 


3 27 


4 o7 


4 87 


$6n 


56g 


58g 


56g 


56g 


58g 


58g 


58g 


6ig 


()Ag 


74g 


5 


2on 


261 


32' 


39' 


44' 


6ol 


8on 


62g 


59g 


59g 


59g 


58g 


6og 


62g 


6 7 g 


74g 


6 


247 


287 


327 


38' 


4 


[/ 


4 87 


8$n 


J2g 


62g 


58g 


58g 


6og 


6 4 g 


6 4 g 


68g 


75g 


8 


2 4 7 


307 




34' 


4 o7 


44"' 


6o7 


II2H 




68g 


66g 




64^ 


66g 






10 


25' 


29 7 


327 


34' 


39' 


407 


5 27 


6 4 l 


u 5 7 


8og 


7 2 g 


68g 


68g 


7g 


yog 


j()g 


12 


267 


2 9 7 


327 


34' 


367 


4 o7 


4 67 


587 


74' 


I20g 


88g 


74^ 


74^ 




7 2 g 


77g 


15 


2 7 7 


3 c7 


33' 


34' 


3 67 


39' 


4 87 


53' 


eo7 


74' 


I 4 ow 


98g 


8og 


j6g 


74g 


8og 


20 


287 


327 


32' 


35' 


3 67 


38' 


44' 


49' 


54' 


6o7 


7 27 


9 o7 


i 3 on 


lOOg 






2 5 


3 o7 


34' 


34' 


35' 


37' 


39' 


43' 


4 67 




5 67 


627 


7 o7 


867 


1507 


QQg 




30 


327 


33' 


35' 


37' 


37' 


39' 


43' 


4 67 


49' 


53' 


6i7 


667 


7 27 


867 






35 


34' 


35' 


3 67 


38' 


39' 




4 27 


45' 


4 87 


52' 


5 67 


627 


697 


7 87 


. . 




40 


35' 


367 


387 


39' 


4 o7 


407 


4 27 


44' 


487 


52' 




6c7 


6 5 7 




. . 




45 


3 87 


387 


397 


39' 


4 


i/ 


427 


44' 


4 67 


49' 




55' 


5 67 










5 


39' 


4 o7 


4 o7 


4 i7 


4 


i/ 


43' 


45' 


47' 


49' 


527 


55' 






. 


. 




55 


407 




4 27 


4 2/ 


43' 


44' 




49' 


52' 








. . 


. . 




60 


427 427 447 447 4 




45' 


4 6l 4 8l 507 











145 
EX-MERIDIAN TABLE No. 1. 

Showing the Reduction at i min. from the Meridian corresponding to the A and B Corrections 

given on Pages 12 to 37 of this Work. 



A and B Reduc- 
Cor. tion. 


A and B Reduc- 
Cor. tion. 


A and B Reduc- 
Cor. tion. 


A andB Reduc- 
Cor. tion. 


A and B Reduc- 
Cor tion. 


A and B Reduc- 
Cor. j tion. 


A and B Reduc- 
Cor. tion. 


I -000 6-213 


1-070 5-918 


I-I 4 5-647 


210 5-396 


I-280 5-165 


T -35 4-95 1 


420 4-752 


I -001 6-209 


1-071 5-914 


1-141 5-643 


211 5-393 


I-28l 5-162 


1-351 4-948 


421 4-749 


1-002 6-205 


1-072 5-910 


1-142 5-639 


212 5-390 


1-282 5-158 


1-352 4-945 


422 4-746 


1-003 6-200 


1-073 5-906 


143 5-636 


213 5-386 


1-283 5-155 


!'353 4-942 


423 4-744 


1-004 6-196 


1-074 5-902 


144 5-632 


2I 4 5-382 


1-284 5-152 


1-354 4-939 


424 4-741 


1-005 6-191 


1-075 5-898 


145 5-628 


215 5-379 


1-285 5-M9 


1-355 4-936 


425 4-738 


1-006 6-187 


1-076 5-894 


I 4 6 5-624 


216 5-376 


1-286 5-146 


I-356 4-933 


426 4-735 


1-007 6-183 


1-077 5-890 


I 47 5-621 


217 5-372 


1-287 5-143 


J -357 4'93 


427 4-733 


I -008 6-178 


1-078 5-886 


I 4 8 5-617 


2i 8 5-369 


1-288 5-140 


I-358 4-927 


428 4-730 


1-009 6-174 


1-079 5-882 


149 5-613 


219 5-365 


1-289 5" I 36 


1-359 4-924 


429 4-727 


i-oio 6-170 


1-080 5-878 


150 5-610 


220 5-362 


1-290 5-133 


1-360 4-921 


430 4-724 


i-oii 6-165 


1-081 5-874 


151 5-606 


221 5-358 


1-291 5-130 


1-361 4-918 


431 4-722 


1-012 6-161 


1-082 5-870 


152 5-602 


222 5-355 


1-282 5-127 


1-362 4-915 


432 4-719 


1-013 6-157 


1-083 5-866 


153 5-599 


223 5-352 


1-293 5-124 


1-363 4-912 


433 4-7I6 


1-014 6-152 


1-084 5-862 


154 5-595 


22 4 5-348 


1-294 5-J2I 


1-364 4-910 


'434 4'7 T 4 


015 6-148 


1-085 5-858 


155 5'59i 


225 5-345 


1-295 5-n8 


1-365 4-907 


435 4-7ii 


016 6-144 


1-086 5-854 


156 5-588 


226 5-342 


1-296 5-115 


1-366 4-904 


436 4-708 


017 6-139 


1-087 5-850 


157 5-584 


227 5-338 


1-297 5' 111 


1-367 4-901 


437 4-705 


018 6-135 


i -088 5-846 


158 5-580 


228 5-335 


1-298 5-108 


1-368 4-898 


438 4-703 


019 6-131 


1-089 5-842 


159 5-577 


229 5-331 


1-299 5' 10 5 


1-369 4-895 


439 4-700 


020 6-127 


1-090 5-838 


i 60 5-573 


230 5-328 


1-300 5-102 


1-370 4-892 


440 4-698 


I-02I 6-122 


1-091 5-834 


161 5-569 


231 5-325 


1-301 5-099 


1-371 4-889 


441 4-695 


1-022 6-1 1 8 


1-092 5-830 


162 5-566 


232 5-321 


1-302 5-096 


1-372 4-886 


442 4-692 


I-O23 6-II4 


1-093 5-826 


163 5-562 


233 5-3i8 


1-303 5- 93 


1-373 4-883 


443 4-690 


1-024 6-no 


1-094 5-823 


164 5-559 


234 5-3 T 5 


1-304 5-089 


1-374 4'88i 


444 4-687 


1-025 6-105 


1-095 5-819 


165 5-555 


235 5-3 11 


1-305 5-086 


1-375 4-878 


445 4-684 


1-026 6-101 


1-096 5-815 


166 5-551 


236 5-3 8 


1-306 5-083 


1-376 4-875 


446 4-682 


1-027 6-097 


1-097 5-811 


167 5-548 


237 5-305 


1-307 5-080 


i'377 4-872 


447 4-679 


1-028 6-093 


1-098 5-807 


168 5-544 


238 5-301 


1-308 5-077 


1-378 4-869 


448 4-676 


1-029 6-089 


1-099 5-803 


J 69 5-54 1 


239 5-298 


1-309 5-074 


1-379 4-866 


449 4-674 


1-030 6-084 


loo 5-799 


- 1 ? 5-537 


240 5-295 


1-310 5-071 


1-380 4-864 


450 4-671 


1-031 6-080 


I01 5-795 


i? 1 5-533 


241 5-291 


1-311 5-068 


1-381 4-861 


451 4-668 


032 6-076 


102 5-791 


!7 2 5-53 


242 5-288 


1-312 5-065 


1-382 4-858 


452 4-666 


033 6-072 


103 5-787 


173 5-526 


243 5-285 


1-313 5-062 


1-383 4-855 


453 4-663 


034 6-067 


104 5-784 


174 5-522 


244 5-282 


I '3 I 4 5-059 


1-384 4-852 


454 4-660 


035 6-063 


105 5-780 


175 5-5I9 


245 5-278 


i '3*5 5-056 


1-385 4-849 


455 4-658 


036 6-059 


106 5-776 


176 5-5I5 


246 5-275 


1-316 5-53 


1-386 4-847 


456 4-655 


037 6-055 


107 5.772 


177 5-512 


247 5-272 


1-317 5-049 


1-387 4-844 


457 4-652 


038 6-050 


-108 5-768 


178 5-508 


248 5-268 


1-318 5-046 


1-388 4-841 


-458 4-650 


1-039 6-046 


109 5.764 


179 5-505 


-249 5-265 


1-319 5-043 


1-389 4-838 


-459 4-647 


1-040 6-042 


-no 5-760 


180 5-501 


250 5-262 


1-320 5-040 


i-39 4-835 


460 4-644 


1-041 6-038 


- 111 5-757 


181 5-497 


251 5-259 


1-321 5-037 


i-39i 4-833 


461 4-642 


1-042 6-033 


H2 5-753 


182 5-494 


-252 5-255 


1-322 5-034 


1-392 4-830 


462 4-639 


1-043 6-029 


"3 5-749 


-183 5-490 


253 5-252 


1-323 5-031 


1-393 4-827 


463 4-637 


1-044 6-025 


"4 5-745 


184 5-487 


-254 5-249 


1-324 5-028 


1-394 4-824 


464 4-634 


1-045 6-021 


"5 5-74 1 


185 5-483 


255 5-246 


1-325 5-025 


1-395 4-821 


465 4-631 


1-046 6-017 


116 5-737 


i 86 5-480 


256 5-242 


1-326 5-022 


1-396 4-819 


466 4-629 


1-047 6-012 


117 6-734 


187 5H76 


257 5-239 


1-327 5-019 


1-397 4-816 


467 4-626 


1-048 6-008 


118 5-730 


188 5-473 


-258 5-236 


1-328 5-016 


1-398 4-813 


468 4-624 


1-049 6-004 


119 5-726 


189 5-469 


259 5-233 


1-329 5-013 


1-399 4-810 


469 4-621 


1-050 6-000 


120 5.722 


190 5-466 


260 5-229 


1-330 5-010 


1-400 4-807 


470 4-618 


1-051 5-996 


i2i 5-718 


191 5-462 


261 5-226 


i-33i 5-7 


1-401 4-805 


471 4-616 


1-052 5-992 


122 5-714 


192 5-459 


262 5-223 


I-332 5-004 


1-402 4-802 


472 4-613 


1-053 5-988 


123 5-711 


193 5H55 


263 5-220 


T '333 5-ooi 


1-403 4-799 


473 4-611 


1-054 5-983 


124 5-707 


-194 5-452 


264 5-216 


J -334 4-998 


1-404 4-796 


474 4-608 


1-055 5-979 


125 5-703 


195 5H48 


265 5-213 


1*335 4'995 


1-405 4-793 


475 4-605 


1-056 5-975 


126 5-699 


196 5-445 


266 5*210 


I-336 4-992 


1-406 4-79 


476 4-603 


1-057 5-97 1 


127 5-696 


197 5-441 


267 5-207 


1-337 4-989 


1-407 4-788 


477 4-600 


1-058 5-967 


128 5-692 


198 5-438 


268 5-203 


1-338 4-986 


1-408 4-785 


478 4-598 


1-059 5-963 


129 5-688 


J 99 5-434 


2O9 5-20O 


1-339 4-983 


1-409 4-782 


'479 4'595 


060 5-959 


130 5-684 


200 5-431 


270 5-197 


1-340 4-980 


1-410 4-779 


480 4-593 


061 5-955 


-131 5-681 


201 5-427 


271 5-194 


1-341 4-977 


1-411 4-776 


481 4-590 


062 5-951 


132 5-677 


202 5-424 


272 5-190 


1-342 4-974 


1-412 4-774 


482 4-588 


063 5-947 


J 33 5-673 


20 3 5-421 


273 5'l87 


1-343 4-971 


1-413 4-771 


483 4-585 


064 5-943 


134 5-669 


20 4 5-417 


274 5-I84 


1-344 4-968 


1-414 4-768 


484 4-582 


065 5-938 


!35 5-666 


20 5 5-414 


275 5-i8i 


1-345 4-965 


1-415 4-765 


485 4-580 


1-066 5-934 


136 5-662 


206 5-410 


276 5-178 


1-346 4-962 


1-416 4-763 


486 4-577 


1-067 5-930 


!37 5-658 


207 5-407 


277 5-174 


1-347 4-959 


1-417 4-760 


487 4-575 


1-068 5-926 


!38 5-654 


208 5-403 


278 5-171 


1-348 4-957 


1-418 4-757 


488 4-572 


1-069 5-922 


!-i39 5-651 


T-209 5-400 


279 5-168 


I- 349 4-954 


1-419 4-755 


489 4-570 



146 
EX-MERIDIAN TABLE No. 1. 

Showing the Reduction at i min. from the Meridian corresponding to the A and B Corrections 
given on Pages 12 to 37 of this Work. 



A and B Reduc- 


A and B Reduc- 


A and B Reduc- 


A and B Reduc- 


A and B Reduc- 


A and B Reduc- 


A and B Reduc- 


Cor. tion. 


Cor. I tion. 


Cor. i tion. 


Cor. tion. 


Cor. tion. 


Cor. tion. 


Cor. tion. 


1-490 4-567 


1-560 4-396 


1-630 4-235 


700 4-085 


77 3-944 


j 
840 3-813 


I-9IO 3-689 


1-491 4-564 


I-56I 4393 


1-631 4-232 


701 4-083 


771 3-942 


841 3-811 


I-9II 3-688 


1-492 4-561 


1-562 4-390 


1-632 4-230 


702 4-081 


772 3-94 1 


8 4 2 3-809 


I-9I2 3-686 


i'493 4"559 


I-563 4-388 


1-633 4-228 


703 4-078 


773 3-939 


843 3-807 


I-9I3 3-684 


1-494 4-557 


1-564 4-386 


1-634 4-226 


704 4-076 


774 3'937 


844 3-805 


1-914 3-682 


J'495 4*554 


I-565 4-383 


1-635 4-224 


-705 4-074 


775 3-935 


845 3-804 


I-9I5 3-681 


1-496 4-552 


1-566 4-381 


1-636 4-221 


706 4-072 


776 3-933 


846 3-802 


1-916 3-679 


1-497 4'549 


1-567 4-379 


1-637 4-219 


707 4-070 


777 3-93 1 


847 3-800 


1-917 3-677 


1-498 4-547 


1-568 4-376 


1-638 4-217 


708 4-068 


778 3-929 


848 3-798 


1-918 3-676 


1-499 4-544 


1-569 4-374 


1-639 4-215 


709 4-066 


779 3-927 


849 3-796 


1-919 3-674 


1-50 4-54 2 


i-57 4-371 


1-640 4-213 


710 4-064 


780 3-925 


850 3-794 


1-920 3-672 


I '5 I 4*539 


I-57 1 4-369 


1-64! 4-211 


711 4-062 


781 3-923 


851 3-793 


I-92I 3-670 


I '52 4-537 


1-572 4-367 


1-642 4-208 


712 4-060 


782 3-921 


852 3-791 


1-922 3-669 


1-503 4-534 


1-573 4-364 


1-643 4-206 


7 T 3 4- 58 


783 3-9I9 


853 3-789 


1-923 3-667 


i-54 4-532 


1-574 4-362 


1-644 4-204 


-714 4-056 


784 3-9I7 


854 3-787 


1-924 3-665 


i-55 4-529 


1-575 4-36o 


1-645 4-202 


'7 J 5 4-054 


785 3-9I5 


855 3-786 


1-925 3-664 


I '56 4-527 


I-576 4-357 


1-646 4-200 


716 4-052 


786 3-914 


856 3-784 


1-926 3-662 


i-57 4-524 


1-577 4*355 


1-647 4-197 


-717 4-050 


787 3-912 


857 3-782 


1-927 3-660 


I '58 4-522 


I-578 4-353 


1-648 4-195 


718 4-048 


788 3-910 


858 3-780 


1-928 3-659 


1-509 4-5I9 


1-579 4-35 


1-649 4-I93 


719 4-046 


789 3-908 


859 3-778 


1-929 3-657 


1-51 4-5I7 


1-580 4-348 


1-650 4-191 


-720 4-044 


790 3-906 


860 3-777 


1-930 3-655 


1-511 4-514 


1-581 4-346 


1-651 4-189 


721 4-042 


791 3-904 


861 3-775 


I'93I 3-654 


1-512 4-512 


1-582 4-343 


1-652 4-186 


722 4-040 


792 3-902 


862 3-773 


1-932 3-652 


I-5I3 4-509 


1-583 4-34 1 


1-653 4-184 


723 4-038 


793 3-900 


863 3-771 


1-933 3-650 


1-514 4-507 


1-584 4-339 


1-654 4-182 


724 4- 36 


794 3-898 


864 3-769 


!'934 3-649 


I-5I5 4-504 


1-585 4-336 


1-655 4' l8 o 


725 4- 34 


795 3-896 


865 3-768 


1-935 3-647 


1-516 4-502 


1-586 4-334 


1-656 4-178 


726 4-031 


796 3-894 


866 3-766 


1-936 3-645 


1-517 4-499 


1-587 4-332 


1-657 4 <J 76 


727 4-029 


'797 3-893 


867 3-764 


J -937 3-644 


1-518 4-497 


1-588 4-329 


1-658 4-174 


728 4-027 


798 3-891 


868 3-762 


I-938 3-642 


i'5 I 9 4H94 


1-589 4-327 


1-659 4' I 7 I 


729 4-025 


799 3-888 


869 3-761 


1-939 3*640 


1-520 4-492 


1-590 4-325 


i -660 4-169 


73 4- 02 3 


800 3-887 


87 3-759 


1-940 3-639 


1-521 4-489 


i-59i 4323 


1-661 4-167 


731 4-021 


801 3-885 


871 3-757 


I-94 1 3-637 


1-522 4-487 


1-592 4-320 


1-662 4-165 


732 4-019 


802 3-883 


872 3-755 


1-942 3-635 


1-523 4-484 


1-593 4'3 l8 


1-663 4- J 63 


733 4' 01 7 


803 3-881 


873 3-753 


1-943 3-634 


1-524 4-482 


1-594 4-3 J 6 


1-664 4-161 


734 4' 01 5 


804 3-879 


874 3-752 


1-944 3-632 


1-525 4-479 


1-595 4'3 J 3 


1-665 4-158 


735 4' 01 3 


805 3-878 


875 3-75 


1-945 3-63 


1-526 4-477 


I-596 4-311 


1-666 4-156 


736 4' 011 


806 3-876 


876 3-748 


1-946 3-629 


1-527 4-475 


1-597 4"39 


1-667 4-154 


737 4-oo9 


-807 3-874 


877 3-746 


1-947 3-627 


1-528 4-472 


1-598 4-307 


1-668 4-152 


738 4-007 


808 3-872 


878 3-745 


1-948 3-625 


1-529 4-470 


1-599 4'34 


1-669 4-150 


739 4'5 


809 3-870 


879 3*743 


1-949 3-624 


1-530 4-467 


1-600 4-302 


1-670 4-148 


-740 4-003 


810 3-868 


880 3-741 


1-950 3-622 


1-531 4-465 


1-601 4-300 


1-671 4-146 


741 4-001 


811 3-866 


881 3-739 


1-951 3-620 


1-532 4-462 


1-602 4-297 


1-672 4-143 


742 3-999 


812 3-864 


882 3-738 


1-952 3-619 


1-533 4H 60 


1-603 4-295 


1-673 4-141 


743 3-997 


813 3-863 


883 3-736 


1-953 3-617 


1-534 4H57 


1-604 4-293 


1-674 4' 1 39 


744 3-995 


814 3-861 


884 3-734 


1-954 3-6I5 


1-535 4-455 


1-605 4-291 


I-675 4 -I 37 


745 3-993 


815 3-859 


885 3-732 


1-955 3-614 


1-536 4*453 


i -606 4-288 


1-676 4-135 


746 3-991 


816 3-857 


886 3-731 


1-956 3-612 


1-537 4-450 


1-607 4-286 


1-677 4 >I 33 


747 3-989 


817 3-855 


887 3-729 


1-957 3-6io 


1-538 4-448 


i -608 4-284 


1-678 4-131 


748 3-988 


818 3-853 


888 3-727 


1-958 3-609 


1*539 4*445 


1-609 4-282 


1-679 4-129 


749 3-986 


819 3-851 


889 3-725 


1-959 3-607 


1-540 4-443 


1-610 4-279 


1-680 4-127 


75 3-984 


820 3-849 


890 3-724 


1-960 3-606 


1-541 4-441 


1-611 4-277 


1-681 4-124 


75 I 3-982 


821 3-848 


891 3-722 


1-961 3-604 


1-542 4-438 


1-612 4-275 


1-682 4-122 


752 3-98o 


822 3-846 


892 3-720 


1-962 3-602 


!'543 4H36 


1-613 4-273 


1-683 4-120 


753 3-978 


823 3-844 


893 3-718 


1-963 3-601 


1-544 4-433 


1-614 4-270 


1-684 4-118 


754 3-976 


824 3-842 


894 3'7!7 


1-964 3-599 


1-545 4-431 


1-615 4-268 


1-685 4-116 


755 3-974 


825 3-840 


895 3-7I5 


i'965 3'597 


1-546 4-429 


1-616 4-266 


1-686 4-114 


756 3-972 


826 3-838 


896 3-713 


1-966 3-596 


1-547 4-426 


1-617 4-264 


1-687 4-112 


757 3-97 


827 3-836 


897 3-7*2 


1-967 3-594 


1-548 4-424 


1-618 4-261 


1-688 4-110 


759 3-968 


828 3-835 


898 3-710 


1-968 3-593 


1-549 4-421 


1-619 4'259 


1-689 4-108 


"759 3-966 


829 3-833 


899 3-708 


1-969 3-59I 


1-550 4-419 


1-620 4-257 


1-690 4-105 


760 3-964 


830 3-831 


900 3-706 


1-970 3-589 


i-55i 4'4 Z 7 


1-621 4-255 


1-691 4-103 


761 3-962 


831 3-829 


901 3-705 


1-971 3-588 


1-552 4-414 


1-622 4-252 


1-692 4-101 


762 3-960 


832 3-827 


902 3-703 


1-972 3-586 


1-553 4'4 12 


1-623 4-250 


1-693 4'99 


763 3-958 


833 3-825 


.903 3-701 


1-973 3-584 


1-554 4-409 


1-624 4-248 


1-694 4'97 


764 3-956 


834 3-824 


904 3-699 


1-974 3-583 


1-555 4 '4 7 


1-625 4-246 


1-695 4"95 


765 3-954 


835 3-822 


905 3-698 


1-975 3-58i 


1-556 4-405 


1-626 4-244 


1-696 4-093 


766 3-952 


836 3-820 


906 3-696- 


1-976 3-580 


1-557 4H 2 


1-627 4-24 1 


1-697 4'9i 


767 3-950 


837 3-818 


907 3-694 


1-977 3-578 


1-558 4-400 


1-628 4-239 


1-698 4-089 


768 3-948 


838 3-816 


908 3-693 


I-97 8 3-576 


1-559 4-398 


1-620 4-237 


1-699 4-087 


769 3-946 


8\g 3-814 


909 3-691 


1-979 3-575 



147 
EX=MERIDIAN TABLE No. I. 

Showing the Reduction at i min. from the Meridian corresponding to the A and B Corrections 
given on Pages 12 to 37 of this Work. 



A and Bj Reduc- 
Cor. ! tion. 


A and B Reduc- 
Cor. tion. 


A and B Reduc- 
Cor. tion. 


A and B Reduc- 
Cor. tion. 


A and B Reduc- 
Cor. tion. 


A and B Reduc- 
Cor. tion 


A and B Reduc- 
Cor. tion. 


980 3'573 


2-050 3-463 


2-120 3-360 


2-190 3-263 


/ / 
2-260 3-170 


2-330 3-084 


2-400 3-001 


981 3-57 1 


2-051 3-462 


2-I2I 3-359 


2-191 3-261 


2-26I 3-169 


2-331 3-082 


2-401 3-000 


982 3-570 


2-052 3-460 


2-122 3-357 


2-192 3-260 


2-262 3-168 


2-332 3-081 


2-402 2-999 


983 3'568 


2-053 3-459 


2-123 3-356 


2-193 3'259 


2-263 3-I67 


2-333 3-o8o 


2-403 2-997 


984 3-567 


2-054 3H57 


2-124 3-355 


2-194 3-257 


2-264 3-I65 


2-334 3-079 


2-404 2-996 


985 3-565 


2-055 3H56 


2-125 3-353 


2-195 3-256 


2-265 3' J 64 


2-335 3-077 


2-405 2-995 


986 3-563 


2-056 3-454 


2-126 3-352 


2-I96 3-255 


2-266 3-163 


2-336 3-076 


2-406 2-994 


987 3-562 


2-057 3H53 


2-127 3-350 


2-197 3-253 


2-267 3'!62 


2*337 3-075 


2-407 2-993 


-988 3-560 


2-058 3-451 


2-128 3-349 


2-198 3-252 


2-268 3-160 


2-338 3-074 


2-408 2-992 


989 3-559 


2-059 3-45 


2-129 3-347 


2-199 3-25 


2-269 3'!59 


2-339 3-073 


2-409 2-990 


990 3-557 


2-060 3-448 


2-13 3-346 


2-200 3-249 


2-270 3-158 


2-340 3-071 


2-410 2-989 


991 3-555 


2-061 3-447 


2 -I3 1 3-345 


2-201 3-248 


2-271 3-156 


2-34 1 3-07 


2-411 2-988 


992 3-554 


2-062 3-445 


2-132 3-343 


2-202 3-246 


2-272 3-155 


2-342 3-069 


2-412 2-987 


993 3-552 


2-063 3-444 


2-133 3-342 


2-203 3-245 


2-273 3- J 54 


2-343 3-068 


2-413 2-986 


994 3-55 1 


2-064 3-442 


2-134 3'34 


2-204 3-244 


2-274 3-153 


2-344 3- 67 


2-414 2-985 


995 3-549 


2-065 3-441 


2-135 3*339 


2-205 3-242 


2-275 3-J5 1 


2-345 3-065 


2-415 2-984 


996 3-547 


2-066 3-439 


2-136 3-337 


2-206 3-24! 


2-276 3-150 


2-346 3-064 


2-416 2-982 


997 3-546 


2-067 3-438 


2-137 3-336 


2-207 3-240 


2-277 3' T 49 


2-347 3-o63 


2-417 2-981 


998 3*544 


2-068 3-436 


2-138 3-335 


2-208 3-238 


2-278 3-148 


2-348 3-062 


2-418 2-980 


999 3-543 


2-069 3-435 


2-139 3-333 


2-209 3-237 


2-279 3-146 


2-349 3-o6i 


2-419 2-979 


2-000 3-541 


2-070 3-433 


2-14 3-332 


2-210 3-236 


2-280 3-145 


2-35 3-059 


2-420 2-978 


2-001 3-539 


2-071 3-432 


2-14! 3'33 


2 -2 1 1 3-234 


2-281 3-144 


2-35 1 3-058 


2-421 2-977 


2-002 3-538 (2-072 3-430 


2-142 3-329 


2-212 3-233 


2-282 3-143 


2-352 3-057 


2-422 2-976 


2-003 3-536 12-073 3-429 


2-143 3-328 


2-213 3-232 


2-283 3-141 


2-353 3- 56 


2-423 2-975 


2-004 3-535 2-074 3-427 


2-144 3-326 


2-214 3-230 


2-284 3-140 


2-354 3-055 


2-424 2-973 


2-005 3-533 


2-075 3-426 


2-145 3-325 


2-215 3-229 


2-285 3-139 


2-355 3-053 


2-425 2-972 


2-006 3-532 


2-076 3-424 


2-146 3-323 


2-216 3-228 


2-286 3-138 


2-356 3-052 


2-426 2-971 


2-007 3-530 


2-077 3-423 


2-147 3-322 


2-2I7 3-226 


2-287 3-136 


2-357 3-05I 


2-427 2-970 


2-008 3-528 


2-078 3-421 


2-148 3-321 


2-2l8 3-225 


2-288 3-135 


2-358 3-05 


2-428 2-969 


2-009 3-527 


2-079 3-420 


2-149 3-3*9 


2-219 3-224 


2-289 3-134 


2-359 3-49 


2-429 2-968 


2-010 3-525 


2-080 3-418 


2-15 3'3 l8 


2-220 3-222 


2-290 3-133 


2-360 3-048 


2-430 2-967 


2-OII 3-524 


2-081 3-417 


2-I5 1 3'3!6 


2-221 3*221 


2-291 3-131 


2-361 3-046 


2-431 2-965 


2-012 3-522 


2-082 3-416 


2-152 3-315 


2-222 3-220 


2-292 3-130 


2-362 3-045 


2-432 2-964 


2-013 3-521 


2-083 3-414 


2-153 3'3M 


2-223 3-2l8 


2-293 3 <I2 9 


2-363 3- 44 


2-433 2-963 


2-014 3-519 


2-084 3-413 


2-154 3'3 12 


2-224 3-217 


2-294 3' 12 8 


2-364 3-043 


2-434 2-962 


2-015 3'5 T 7 


2-085 3-411 


2-155 3-3 11 


2-225 3-2I6 


2-295 3-126 


2-365 3-042 


2-435 2-961 


2-016 3-516 


2-086 3-410 


2-156 3-3 9 


2-226 3-2I5 


2-296 3-125 


2-366 3-040 


2-436 2-960 


2-017 3-514 


2-087 3-408 


2-157 3'3 o8 


2-227 3-2I3 


2-297 3' 12 4 


2-367 3-039 


2-437 2-959 


2-018 3-513 


2-088 3-407 


2-158 3'37 


2-228 3-212 


2-298 3-123 


2-368 3-038 


2-438 2-958 


2-019 3-5 11 


2-089 3'45 


2-159 3'35 


2-229 3-211 


2-299 3-121 


2-369 3- 37 


2-439 2-957 


2-020 3-510 


2-090 3-404 


2-160 3-304 


2-230 3-209 


2-300 3-120 


2-37 3-036 


2-440 2-955 


2-021 3-508 


2-091 3-402 


2-161 3-302 


2-23I 3-208 


2-301 3-119 


2-37 1 3-035 


2-441 2-954 


2-022 3-506 


2-092 3-401 


2-162 3-301 


2-232 3-207 


2-302 3-118 


2-372 3- 33 


2-442 2-953 


2-023 3-505 


2-093 3-399 


2-163 3-300 


2-233 3-205 


2-303 3-116 


2-373 3-032 


2-443 2-952 


2-024 3-503 


2-094 3-398 


2-164 3-298 


2-234 3-204 


2'34 3' XI 5 


2-374 3-03 1 


2-444 2-951 


2-025 3-502 


2-095 3-396 


2-165 3-297 


2-235 3-203 


2'35 3 >IT 4 


2-375 3-03 


2-445 2-950 


2-026 3-500 


2-096 3-395 


2-166 3-296 


2-236 3-201 


2-306 3-113 


2-376 3-029 


2-446 2-949 


2-027 3-499 


2-097 3-394 


2-167 3-294 


2-237 3-200 


2-307 3' 112 


2-377 3-028 


2-447 2-948 


2-028 3-497 


2-098 3-392 


2-168 3-293 


2-238 3-I99 


2-308 3-110 


2-378 3-026 


2-448 2-947 


2-029 3-496 


2-099 3-39I 


2-169 3'29i 


2-239 3- J 97 


2-309 3-109 


2-379 3-025 


2-449 2-945 


2-030 3-494 


2-100 3-389 


2-170 3-290 


2-240 3-196 


2-310 3-108 


2-380 3-024 


2-450 2-944 


2-031 3-493 


2-IOI 3-388 


2-171 3-289 


2-241 3-195 


2-311 3' 10 7 


2-381 3-023 


2-451 2-943 


2-032 3-491 


2-102 3-386 


2-172 3-287 


2-242 3-194 


2-312 3-105 


2-382 3-022 


2-452 2-942 


2-033 3'49 


2-103 3-385 


2-173 3-286 


2-243 3-192 


2-313 3' 10 4 


2-383 3-021 


2-453 2-941 


2-034 3-488 


2-I0 4 3-383 


2-174 3-284 


2-244 3-191 


2-314 3-103 


2-384 3- OI 9 


2-454 2-940 


2-035 3H86 


2-105 3-382 


2-175 3-283 


2-245 3-190 


2-3 J 5 3' 102 


2-385 3- l8 


2-455 2-939 


2-036 3-485 


2-106 3-380 


2-176 3-282 


2-246 3-188 


2-316 3-101 


2-386 3-017 


2-456 2-938 


2-037 3-483 


2-107 3-379 


2-177 3-280 


2-247 3-187 


2-317 3- 99 


2-387 3-016 


2-457 2-937 


2-038 3-482 


2-108 3-378 


2-178 3-279 


2-248 3-186 


2-318 3-098 


2-388 3-015 


2-458 2-935 


2-039 3-480 


2-109 3-376 


2-179 3-278 


2-249 3 <l8 4 


2-319 3-097 


2-389 3 >OI 4 


2-459 2-934 


2-040 3-479 2 -1 10 3-375 


2-180 3-276 


2-250 3-183 


2-320 3-096 


2-390 3-012 


2-460 2-933 


2-0 4 I 3-477 


2-III 3-373 


2-181 3-275 


2-251 3-182 


2-321 3-094 


2-391 3-011 


2-461 2-932 


2-0 4 2 3-476 


2-II2 3-372 


2-182 3-274 


2-252 3-181 


2-322 3-093 


2-392 3' 010 


2-462 2-931 


2-043 3H74 


2-113 3-37 


2-183 3-272 


2-253 3-179 


2-323 3- 92 


2-393 3-o 9 


2-463 2-930 


2-44 3H73 


2-114 3-369 


2-184 3-271 


2-254 3'i78 


2-324 3-091 


2-394 3-o8 


2-464 2-929 


2-045 3-471 


2-115 3-367 


2-185 3-269 


2-255 3-177 


2-325 3-9 


2-395 3-o o 7 


2-465 2-928 


2-046 3-470 


2-116 3-366 


2-186 3-268 


2-256 3-176 


2-326 3-088 


2-396 3-o o 5 


2-466 2-927 


2-047 3-468 


2-117 3-365 


2-187 3-267 


2-257 3-174 


2-327 3-087 


2-397 3-o 4 


2-467 2-925 


2-048 3-457 


2-118 3-363 


2-188 3-265 


2-258 3-173 


2-328 3-086 


2-398 3-003 


2-468 2-924 


2-049 3-465 


2-119 3-362 


2-189 3-264 


2-259 V T 72 


2-329 3-085 


2-399 3" 002 


2-469 2-923 



148 
EX=MERIDIAN TABLE 



No. 



Showing the Reduction at i min. from the Meridian corresponding to the A and B Corrections 
given on Pages 12 to 37 of this Work. 



A and B Reduc- i 
Cor. tion. 


\ and B Reduc- i 
Cor. tion. 


V and B Reduc- A and B Reduc- i 
Cor. tion. Cor. tion. 


\ and B Reduc- 
Cor. tion. 


\ and B Reduc- 
Cor. tion. 


A and B Reduc- 
Cor. tion. 


2-470 2-922 


2-540 2-847 


2-660 2-727 


2-800 2-598 


2-940 2-482 


3-080 2-374 


3-220 2-276 


2-471 2-Q2I 


2-541 2-846 


2-662 2-725 


2-802 2-597 


2-942 2-480 


3-082 2-373 


3-222 2-274 


2-472 2-920 


2-542 2-845 


2-664 2-723 


2-804 2-595 


2-944 2-478 


3-084 2-371 


3-224 2-273 


2-473 2-919 


2-543 2-844 


2-666 2-721 


2-806 2-593 


2-946 2-477 


3-086 2-370 


3-226 2-272 


2-474 2-918 


2-544 2-843 


2-668 2-719 


2-808 2-592 


2-948 2-475 


3-088 2-368 


3-228 2-270 


2-475 2-9I7 


2-545 2-842 


2-670 2-717 


2-810 2-590 


2-950 2-474 


3-090 2-367 


3-230 2-269 


2-476 2-916 


2-546 2-841 


2-672 2-715 


2-812 2-588 


2-952 2-472 


3-092 2-366 


3-232 2-267 


2-477 2-914 


2-547 2-840 


2-674 2-714 


2-814 2-586 


2-954 2-470 


3-094 2-364 


3-234 2-266 


2-478 2-9I3 


2-548 2-839 


2-676 2-712 


2-816 2-585 


2-956 2-469 


3-096 2-363 


3-236 2-265 


2-479 2-912 


2-549 2-838 


2-678 2-710 


2-818 2-583 


2-958 2-467 


3-098 2-361 


3-238 2-264 


2-480 2-911 


2-55 2-837 


2-680 2-708 


2-820 2-581 


2-960 2-466 


3-100 2-360 


3-240 2-262 


2-481 2-910 


2-551 2-836 


2-682 2-706 


2-822 2-579 


2-962 2-464 


3-102 2-358 


3-242 2-26I 


2-482 2-909 


2-552 2-835 


2-684 2-704 


2-824 2-578 


2-964 2-463 


3-104 2-357 


3-244 2-260 


2-483 2-908 


2-553 2-834 


2-686 2-702 


2-826 2-576 


2-966 2-461 


3-106 2-355 


3-246 2-258 


2-484 2-907 


2-554 2-833 


2-688 2-700 


2-828 2-574 


2-968 2-459 


3-108 2-354 


3-248 2-257 


2-485 2-906 


2-555 2-832 


2-690 2-698 


2-830 2-573 


2-970 2-458 


3-110 2-352 


3-250 2-256 


2-486 2-905 


2-556 2-831 


2-692 2-696 


2-832 2-571 


2-972 2-456 


3-112 2-351 


3-252 2-254 


2-487 2-904 


2-557 2-830 


2-694 2-694 


2-834 2-569 


2-974 2-455 


3-114 2-350 


3-254 2-253 


2-488 2-903 


2-558 2-829 


2-696 2-693 


2-836 2-567 


2-976 2-453 


3-116 2-348 


3-256 2-252 


2-489 2-901 


2-559 2-828 


2-698 2-691 


2-838 2-566 


2-978 2-452 


3-118 2-347 


3-258 2-250 


2-490 2-900 


2-560 2-826 


2-700 2-689 


2-840 2-564 


2-980 2-450 


3-120 2-345 


3-260 2-249 


2-491 2-899 


2-562 2-824 


2-702 2-687 


2-842 2-562 


2-982 2-448 


3-122 2-344 


3-262 2-248 


2-492 2-898 


2-564 2-822 


2-704 2-685 


2-844 2-561 


2-984 2-447 


3-124 2-342 


3-264 2-246 


2-493 2-897 


2-566 2-820 


2-706 2-683 


2-846 2-559 


2-986 2-445 


3-126 2-341 


3-266 2-245 


2-494 2-896 


2-568 2-818 


2-708 2-681 


2-848 2-557 


2-988 2-444 


3-128 2-339 


3-268 2-244 


2-495 2-895 


2-570 2-816 


2-710 2-680 


2-850 2-556 


2-990 2-442 


3 -I 3 2-338 


3-270 2-242 


2-496 2-894 


2-572 2-814 


2-712 2-678 


2-852 2-554 


2-992 2-441 


3-132 2-337 


3-272 2-241 


2-497 2-893 


2-574 2-812 


2-714 2-676 


2-854 2-552 


2-994 2-439 


3-134 2-335 


3-274 2-240 


2-498 2-892 


2-576 2-810 


2-716 2-674 


2-856 2-551 


2-996 2-438 


3-136 2-334 


3-276 2-238 


2-499 2-891 


2-578 2-808 


2-718 2-672 


2-858 2-549 


2-998 2-436 


3-138 2-332 


3-278 2-237 


2-500 2-890 


2-580 2-806 


2-720 2-670 


2-860 2-547 


3-000 2-435 


3-140 2-331 


3-280 2-236 


2-501 2-889 


2-582 2-804 


2-722 2-668 


2-862 2-546 


3-002 2-433 


3-142 2-330 


3-282 2-234 


2-502 2-888 


2-584 2-802 


2-724 2-667 


2-864 2-544 


3-004 2-431 


3-144 2-328 


3-284 2-233 


2-503 2-886 


2-586 2-800 


2-726 2-665 


2-866 2-542 


3-006 2-430 


3-146 2-327 


3-286 2-232 


2-504 2-885 


2-588 2-797 


2-728 2-663 


2-868 2-540 


3-008 2-428 


3-148 2-325 


3-288 2-231 


2-505 2-884 


2-590 2-796 


2-730 2-661 


2-870 2-539 


3-010 2-427 


3-150 2-324 


3-290 2-229 


2-506 2-883 


2-592 2-794 


2-732 2-659 


2-872 2-537 


3-012 2-425 


3-152 2-322 


3-292 2-228 


2-507 2-882 


2-594 2-792 


2-734 2-657 


2-874 2-535 


3-014 2-424 


3-154 2-321 


3-294 2-227 


2-508 2-881 


2-596 2-790 


2-736 2-656 


2-876 2-534 


3-016 2-422 


3-156 2-320 


3-296 2-225 


2-509 2-880 


2-598 2-788 


2-738 2-654 


2-878 2-532 


3-018 2-421 


3-158 2-318 


3-298 2-224 


2-510 2-879 


2-600 2-786 


2-740 2-652 


2-880 2-530 


3-020 2-419 


3-160 2-317 


3-300 2-22j 


2-511 2-878 


2-602 2-784 


2-742 2-650 


2-882 2-529 


3-022 2-418 


3-162 2-315 


3-302 2-221 


2-512 2-877 


2-604 2-782 


2-744 2-648 


2-884 2-527 


3-024 2-416 


3-164 2-314 


3-304 2-220 


2-513 2-876 


2-606 2-780 


2-746 2-646 


2-886 2-525 


3-026 2-415 


3-166 2-313 


3-306 2-219 


2-514 2-875 


2-608 2-778 


2-748 2-645 


2-888 2-524 


3-028 2-413 


3-168 2-311 


3-308 2-218 


2-515 2-874 


2-610 2-776 


2-750 2-643 


2-890 2-522 


3-030 2-412 


3-170 2-310 


3-3IO 2-216 


2-516 2-873 


2-612 2-774 


2-752 2-641 


2-892 2-521 


3-032 2-410 


3-172 2-308 


3-3I2 2-215 


2-517 2-871 


2-614 2-772 


2-754 2-639 


2-894 2-519 


3-034 2-409 


3-174 2-307 


3-314 2-214 


2-518 2-870 


2-616 2-770 


2-756 2-637 


2-896 2-517 


3-036 2-407 


3-176 2-306 


3-316 2-212 


2-519 2-869 


2-618 2-768 


2-758 2-636 


2-898 2-516 


3-038 2-406 


3-178 2-304 


3-318 2-2II 


2-520 2-868 


2-620 2-766 


2-760 2-634 


2-900 2-514 


3-040 2-404 


3-180 2-303 


3-320 2-210 


2-521 2-867 


2-622 2-764 


2-762 2-632 


2-902 2-512 


3-042 2-403 


3-182 2-302 


3-322 2-209 


2-522 2-866 


2-624 2-762 


2-764 2-630 


2-904 2-511 


3-044 2-401 


3-184 2-300 


3-324 2-207 


2-523 2-865 


2-626 2-760 


2-766 2-628 


2-906 2-509 


3-046 2-400 


3-186 2-299 


3-326 2-206 


2-524 2-864 


2-628 2-758 


2-768 2-627 


2-908 2-507 


3-048 2-398 


3-188 2-297 


3-328 2-205 


2-525 2-863 


2-630 2-756 


2-770 2-625 


2-910 2-506 


3-050 2-397 


3-190 2-296 


3-330 2-204 


2-526 2-862 


2-632 2-754 


2-772 2-623 


2-912 2-504 


3-052 2-395 


3-192 2-295 


3-332 2-202 


2-527 2-861 


2-634 2-752 


2-774 2-621 


2-914 2-503 


3'54 2-394 


3-194 2-293 


3-334 2-201 


2-528 2-860 


2-636 2-750 


2-776 2-620 


2-916 2-501 


3-056 2-392 


3-196 2-292 


3-336 2-200 


2-529 2-859 


2-638 2-748 


2-778 2-618 


2-918 2-499 


3-058 2-391 


3-198 2-291 


3-338 2-199 


2-53 2-858 


2-640 2-746 


2-780 2-616 


2-920 2-498 


3-060 2-389 


3-200 2-289 


3-340 2-197 


2-53 1 2-857 


2-642 2-744 


2-782 2-614 


2-922 2-496 


3-062 2-388 


3-202 2-288 


3-342 2-196 


2-532 2-856 


2-644 2-742 


2-784 2-613 


2-924 2-494 


3-064 2-386 


3-204 2-286 


3-344 2-195 


2-533 2-855 


2-646 2-740 


2-786 2-611 


2-926 2-493 


3-066 2-385 


3-206 2-285 


3-346 2-193 


2-534 2-854 


2-648 2-738 


2-788 2-609 


2-928 2-491 


3-068 2-383 


3-208 2-284 


3-348 2-192 


2-535 2-853 


2-650 2-737 


2-790 2-607 


2-93 2-490 


3-070 2-382 


3-210 2-282 


3-350 2-191 


2-536 2-852 


2-652 2-735 


2-792 2-605 


2-932 2-488 


3-072 2-380 


3-212 2-281 


3-352 2-190 


2-537 2-850 


2-654 2-733 


2-794 2-604 


2-934 2-486 


3-074 2-379 


3-214 2-280 


3-354 2-188 


2-538 2-849 


2-656 2-731 


2-796 2-602 


2-936 2-485 


3-076 2-377 


3-216 2-278 


3-356 2-187 


2-539 2-848 


2^658 2-729 


2-798 2-600 


2-938 2-483 


3-078 2-376 


3-218 2-277 


3-358 2-186 



149 
EX-MERIDIAN TABLE No. 1. 

the Reduction at i min. from the Meridian corresponding to the A and B Corrections 
given on Pages 12 to 37 of this Work. 



A and B 
Cor. 


Reduc- 
tion. 


AandB 
Cor. 


Reduc- 
tion. 


A and B 

Cor. 


Reduc- 
tion. 


AandB 
Cor. 


Reduc- 
tion. 


A and B 
Cor. 


Reduc- 
tion. 


AandB 
Cor. 


Reduc- A and B 
tion. j Cor. 


Reduc- 
tion. 


3-360 


2-185 


3-50 


2-IOI 


3-640 


/ 
2-023 


3-780 


951 


3-920 


8 / 8 3 


4-060 


-820 


4-200 


761 


3362 


2-183 


3-502 


2-100 


3-642 


2*022 


3-782 


95 


3-922 


882 


4-062 


819 


4-202 


7 60 


3-364 


2-I82 


3-504 


2-098 


3*644 


2-021 


3-784 


949 


3-924 


-881 


4-064 


818 


4-204 


759 


3-366 


2-181 


3-506 


2-097 


3-646 


2-02O 


3-786 


948 


3-926 


880 


4-066 


818 


4-206 


759 


3-368 


2-180 


3-508 


2-096 


3-648 


2-019 


3-788 


947 


3-928 


879 


4-068 


817 


4-208 


758 


3-370 


2-178 


3-510 


2-095 


3-650 


2-018 


3-790 


946 


3-93 


878 


4-070 


816 


4-210 


757 


3-372 


2-177 


3-512 


2-094 


3-652 


2-OI7 


3-792 


945 


3-932 


878 


4-072 


-815 4-212 


756 


3-374 


2-176 


3-5 J 4 


2-093 


3-654 


2-016 


3-794 


944 


3-934 


877 


4-074 


-814 


4-214 


755 


3'376 


2-175 


3-5I6 


2-092 


3-656 


2-015 


3-796 


943 


3-936 


876 


4-076 


813 


4-216 


755 


3378 


2-173 


3-5I8 


2-090 


3-658 


2-014 


3-798 


942 


3-938 


875 


4-078 


812 


4-218 


754 


3-380 


2-172 


3-520 


2-089 


3-660 


2-012 


3- 800 


.941 


3*94 


874 


4-080 


811 


4-220 


753 


3-382 


2-171 


3-522 


2-088 


3-662 


2-OII 


3-802 


94 


3-942 


873 


4-082 


811 


4^222 


752 


3-384 


2-170 


3-524 


2-087 


3-664 


2-OIO 


3-804 


939 


3-944 


-872 


4-084 


810 


4-224 


751 


3-386 


2-169 


3-526 


2-086 


3-666 


2-009 


3-806 


938 


3-946 


871 


4-086 


809 


4-226 


751 


3-388 


2-167 


3-528 


2-085 


3-668 


2'008 


3-808 


937 


3-948 


870 


4-088 


808 


4-228 


750 


3-390 


2-166 


3-53 


2-084 


3-670 


2-007 


3-810 


936 


3-95 


869 


4-090 


-807 


4-230 


749 


3392 


2-165 


3-532 


2-083 


3-672 


2-006 


3-812 


935 


3-952 


868 


4-092 


806 


4-232 


748 


3-394 


2-164 


3-534 


2-081 


3-674 


2-005 


3-814 


934 


3-954 


867 


4-094 


805 


4-234 


747 


3-396 


2-162 


3-536 


2-080 


3-676 


2-004 


3-816 


933 


3-056 


867 


4-096 


805 


4-236 


747 


3-398 


2-161 


3-538 


2-079 


3-678 


2-003 


3-818 


932 


3-958 


866 


4-098 


804 


4-238 


.746 


3-400 


2 -I 60 


3-54 


2-078 


3-680 


2-002 


3-820 


93 1 


3-960 


865 


4. zoo 


803 


4-240 


'745 


3-402 


2-159 


3-542 


2-077 


3-682 


2-001 


3-822 


93 


3-962 


864 


4-102 


802 


4-242 


744 


3'44 


2-I58 


3-544 


2-076 


3-684 


2-000 


3-824 


929 


3-964 


863 


4-104 


-801 


4-244 


743 


3-406 


2-I56 


3-546 


2-075 


3-686 


1-999 


3-826 


-928 


3-966 


-862 


4-106 


800 


4-246 


743 


3-408 


2-155 


3-548 


2-074 


3-688 


1-998 


3-828 


927 


3.968 


861 


4-108 


799 


4-248 


742 


3.410 


2-154 


3-55 


2-072 


3-690 


1-997 


3-83 


-926 


3.970 


860 


4-110 


799 


4-250 


741 


3.412 


2-153 


3-552 


2-071 


3-692 


1-996 


3-832 


925 


3-972 


859 


4-112 


798 


4-252 


74 


3'4 T 4 


2-I52 


3-554 


2-070 


3-694 


1-995 


3-834 


924 


3-974 


858 


4-114 


797 


4-254 


739 


V4 l6 


2T50 


3-556 


2-069 


3-696 


1-994 


3-836 


923 


3-976 


857 


4-116 


796 


4^56 


739 


3-418 


2T49 


3-558 


2-068 


3-698 


1-993 


3-838 


922 


3-978 


857 


4-118 


795 


4-258 


738 


3-420 


2T48 


3-56o 


2-067 


3-700 


1-992 


3-840 


921 


3-98o 


856 


4-120 


794 


4-260 


737 


3-422 


2-147 


3-562 


2-066 


3.702 


1-990 


3-842 


-920 


3-982 


855 


4" 122 


794 


4-262 


736 


3H 2 4 


2-145 


3-564 


2-065 


3-7 4 


1-989 


3-844 


919 


3-984 


854 


4-124 


793 


4-264 


735 


3H26 


2-144 


3-566 


2-063 


3.706 


1-988 


3-846 


-918 


3-986 


853 


4-126 


792 


4 -266 


735 


3.428 


2-143 


3-568 


2-062 


3-70.8 


1-987 


3-848 


917 


3-988 


852 


4-128 


-791 


4-268 


734 


3'43 


2-I42 


3-57 


2-061 


3-710 


1-986 


3-850 


916 


3-990 


851 


4' 1 3 


790 


4-270 


733 


3H32 


2-I 4 I 


3-572 


2-060 


3.712 


1-985 


3-852 


915 


3-992 


851 


4- J 32 


789 


4-272 


732 


3H34 


2-139 


3-574 


2-059 


3'7M 


1-984 


3-854 


914 


3-994 


849 


4' 1 34 


788 


4-274 


732 


5*436 


2-138 


3-576 


2-058 


3-716 


1-983 


3-856 


913 


3-996 


-848 


4-136 


788 


4-276 


73 1 


3H38 


2-137 


3-578 


2-057 


3-718 


1-982 


3-858 


912 


3-998 


-848 


4-I38 


787 


4-278 


73 


3*44 


2-I36 


3-58o 


2-056 


3-720 


1-981 


3-860 


.911 


4-000 


847 


4-140 


786 


4-280 


729 


3-442 


2-135 


3-582 


2-055 


3-722 


1-980 


3-862 


911 


4-002 


846 


4-142 


785 


4-282 


728 


3*444 


2-134 


3-584 


2-054 


3-724 


1-979 


3-864 


910 


4-004 


8 4 5 


4-144 


784 


4-284 


728 


3H46 


2-I32 


3-586 


2-052 


3.726 


1-978 


3-866 


909 


4-006 


844 


4-146 


783 


4-286 


727 


3H48 


2T3I 


3-588 


2-051 


3-728 


1-977 


3-868 


908 


4-008 


8 4 3 


4-148 


783 


4-288 


726 


3H50 


2-130 


3-590 


2-050 


3-73 


1-976 


3-870 


907 


4-010 


842 


4 <I 5 


-782 


4-290 


725 


3H52 


2-129 


3-592 


2-049 


3-732 


1-975 


3-872 


906 


4-012 


-841 


4" J 52 


-781 


4-292 


725 


3-454 


2-128 


3-594 


2-048 


3-734 


1-974 


3-874 


905 


4-014 


840 


4- J 54 


-780 


4-294 


724 


3-456 


2-126 


3-596 


2-047 


3-736 


1-973 


3-876 


-904 


4-016 


839 


4' T 56 


779 


4-296 


723 


3-458 


2-125 


3-598 


2-046 


3-738 


1-972 


3-878 


9^3 


4-018 


839 


4'!58 


778 


4-298 


-722 


3.460 


2-124 


3-600 


2-045 


3-74 


1-971 


3-880 


902 


4-020 


838 


4-160 


778 


4-300 


721 


3*462 


2-123 


3-602 


2-044 


3-742 


1-970 


3-882 


901 


4-022 


837 


4-162 


'777 


4-302 


721 


3H64 


2-122 


3-604 


2-043 


3-744 


1-969 


3-884 


900 


4-024 


836 


4-164 


776 


4-304 


720 


3H66 


2-I2I 


3- 606 


2-041 


3-746 


1-968 


3-886 


899 


4-026 


835 


4-166 


775 


4.306 


-719 


3.468 


2-II9 


3-608 


2-040 


3-748 


1-967 


3-888 


-898 


4-028 


834 


4-168 


774 


4.308 


718 


3-47 


2-II8 


3-610 


2-039 


3-75 


1-966 


3-890 


897 


4-030 


833 


4-170 


773 


4'3 10 


717 


3H72 


2-II7 


3 '6i 2 


2-038 


3-752 


1-965 


3-892 


896 


4-032 


832 


4-172 


773 


4'3 12 


717 


3-474 


2-116 


3-614 


2-037 


3-754 


1-964 


3-894 


895 


4'34 


831 


4' J 74 


772 


4-3I4 


716 


3H76 


2-II5 


3-616 


2-036 


3-756 


1-963 


3-896 


894 


4-036 


831 


4-176 


.771 


4-316 


7*5 


3H78 


2-II4 


3-618 


2-035 


3-758 


1-962 


3-898 


1-893 


4-038 


-830 


4-178 


.770 


4-3i8 


714 


3-480 


2-II2 


3-620 


2-034 


3-760 


1-961 


3-900 


1-892 


4-040 


829 


4-180 


769 


4-320 


7*3 


3-482 


2-III 


3-622 


2-033 


3-762 


1-960 


3-902 


1-892 


4-042 


828 


4-182 


768 


4-322 


713 


3-484 


2-IIO 


3-624 


2-032 


3-764 


1-959 


3-904 


891 


4-044 


827 


4-184 


768 


4-324 


712 


3-486 


2-109 


3-626 


2-031 


3-766 


I-958 


3-906 


890 


4-046 


-826 


4-186 


767 


4-326 


711 


3.488 


2-108 


3-628 


2-030 


3-768 


1-957 


3-908 


-889 


4-048 


825 


4-188 


-766 


4'328 


710 


3H90 


2-107 


3-63 


2-029 


3-770 


1-956 


3.910 


-888 


4-050 


824 


4-190 


765 


4-33 


710 


3H92 


2-105 


3-632 


2-027 


3-772 


1-955 


3.912 


887 


4-052 


824 


4-192 


764 


4-332 


-709 


3-494 


2-104 


3-634 


2-026 


3-774 


1-954 


3-9I4 


886 


4'54 


823 


4-194 


764 


4-334 


708 


3-496 


2-I03 


3-636 


2-025 3-776 


1-953 


3.916 


885 


4-056 


822 


4-196 


763 


4-336 


707 


3-498 


2*102 


VGvS 


7-024 3-778 


1 '952 


3-918 


884 


4-058 


821 


4-198 


762 4-338 


77 



150 
EX=MERIDIAN TABLE 



No. 



Showing the Reduction at i min. from the Meridian corresponding to the A and B Corrections 
given on Pages 12 to 37 of this Work. 



A and B Reduc- 
Cor. tion. 


A and B Reduc- 
Cor. tion. 

i 


A and B 
Cor. 


Reduc- 
tion. 


AandB 
Cor. 


Reduc- 
tion. 


AandB 
Cor. 


Reduc- A and B 
tion. Cor. 


Reduc- 
tion. 


AandB 
Cor. 


Reduc- 
tion. 


4-340 -706 


4-480 1-654 


4-620 


605 


4-760 


559 


4-900 


I'5I5 


5-50 


I '3 / 53 


6-200 


/ 
202 


4-342 -705 


4-482 1-653 


4-622 


604 


4-762 


558 


4-902 


I '5 I 4 


5'5 10 


J -35 


6-210 


2OO 


4-344 -74 


4-484 1-652 


4-624 


604 


4-764 


557 


4-904 


I '5 I 4 


5-520 


!'348 


6-220 


198 


4346 -703 


4-486 1-652 


4-626 


603 


4-766 


557 


4-906 


I'5I3 


5'53 


I- 345 


6-230 


196 


4-348 -703 


4-488 1-651 


4-628 


-602 


4-768 


556 


4-908 


I-5I3 


5'54 


1-343 


6-240 


194 


4.350 -702 


4-490 1-650 


4-630 


O02 


4-770 


555 


4-910 


1-512 


5-550 


I '34 I 


6-250 


192 


4-352 -701 


4-492 1-649 


4-632 


60 1 


4-772 


'555 


4-912 


1-511 


5'56o 


1-338 


6-260 


191 


4-354 '7 00 


4-494 1-649 


4-634 


600 


4*774 


'554 


4-914 


1-511 


5-57 


I-336 


6-270 


189 


4-356 -700 


4-496 1-648 


4-636 


599 


4-776 


554 


4-916 


1-510 


5-58o 


!'333 


6-280 


I8 7 


4-358 "699 


4-498 1-647 


4-638 


599 


4-778 


553 


4-918 


1-510 


5-590 


I '33 I 


6-290 


I8 5 


4-360 -698 


4-500 1-647 


4-640 


598 


4-780 


552 


4-920 


1-509 


5-600 


1-329 


6-300 


183 


4-362 -697 


4-502 1-646 


4-642 


597 


4-782 


552 


4-922 


1-508 


5-610 


1-326 


6-310 


181 


4-364 -697 


4-504 1-645 


4-644 


597 


4-784 


55i 


4-926 


1-507 


5-620 


1-324 


6-320 


179 


4-366 1-696 


4-506 1-645 


4-646 


596 


4-786 


55 


4-93 


1-506 


5-630 


1-322 


6-330 


177 


4-368 1-695 


4-508 1-644 


4-648 


595 


4-788 


55 


4-940 


1-503 


5-64 


1-320 


6-340 


176 


4-370 1-694 


4-510 1-643 


4-650 


595 


4-790 


549 


4-950 


1-500 


5-650 


I '3 I 7 


6-35 


' r 74 


4-372 1-694 


4-512 1-642 


4-652 


594 


4-792 


548 


4-960 


1-497 


5-660 


I-3I5 


6-360 


172 


4-374- 1-693 


4-514 1-642 


4-654 


593 


4-794 


548 


4-97 


1-494 


5-670 


i'3i3 


6-370 


170 


4-376 1-692 


4-516 1-641 


4*656 


593 


4-796 


547 


4-980 


1-491 


5-680 


1-310 


6-380 


168 


4.378 1-691 


4-518 1-640 


4-658 


592 


4-798 


547 


4-990 


1-488 


5-690 


1-308 


6-390 


167 


4-380 1-691 


4-520 1-640 


4-660 


591 


4-800 


546 


5-000 


1-485 


5-70 


1-306 


6-400 


165 


4-382 i ; 69O 


4-522 1-639 


4-662 


59i 


4-802 


545 


5-010 


1-482 


5-710 


J^OS 


6-410 


163 


4-384 -689 


4-524 1-638 I 4-664 


590 


4-804 


545 


5-020 


1-480 


5-720 


1-301 


6-420 


161 


4-386 -688 


4-526 1-637 


4-666 


589 


4-806 


544 


5-030 


1-477 


5-73 


1-299 


6-43 


159 


4-388 -688 


4-528 1-637 


4-668 


589 


4-808 


544 


5-040 


J'474 


5-74 


1-297 


6-440 


158 


4-390 -687 


4-53 1-636 


4-670 


588 


4-810 


543 


5-050 


1-471 


5-75 


1-294 


6-450 


-156 


4-392 -686 


4-532 1-635 


4-672 


587 


4-812 


542 


5-060 


1-468 


5-76o 


1-292 


6-460 


J 54 


4-394 -685 


4-534 !-635 


4-674 


587 


4-814 


542 


5-070 


1-465 


5-77 


1-290 


6-470 


152 


4-396 -685 


4-536 1-634 


4-676 


586 


4-816 


541 


5-080 


1-462 


5-78o 


1-288 


6-480 


150 


4-398 -684 


4-538 1-633 


4-678 


585 


4-818 


54 


5-090 


1-460 


5-790 


1-286 


6-490 


149 


4-400 -683 


4-540 1-632 


4-680 


585 


4-820 


54 


5-100 


!'457 


5-800 


1-284 


6-500 


-147 


4-402 -682 


4-542 1-632 


4-682 


584 


4-822 


539 


5-110 


!'454 


5-810 


1-281 


6*510 


J 45 


4-404 -682 


4-544 1-631 


4-684 


583 


4-824 


538 


5-120 


i-45i 


5-820 


1-279 


6-520 


144 


4-406 -681 


4-546 1-630 


4-686 


58 3 


4-826 


538 


5-13 


1-448 


5-830 


1-277 


6-53 


142 


4-408 -680 


4-548 1-630 


4-688 


582 


4-828 


537 


5-14 


1-446 


5-840 


1-275 


6-540 


140 


4-410 -679 


4-550 1-629 


4-690 


581 


4-830 


537 


5-15 


J -443 


5-850 


1-273 


6-550 


-138 


4-412 -679 


4-552 1-628 


4-692 


581 


4-832 


536 


5-160 


1-440 


5-860 


1-270 


6-560 


137 


4-414 -678 


4-554 1-628 


4-694 


580 


4-834 


'535 


5-170 


I- 437 


5-870 


1-268 


6-57 


135 


4-416 -677 


4-556 1-627 


4-696 


'579 


4-836 


535 


5-180 


1*435 


5-880 


1-266 


6-580 


133 


4-418 -676 


4-558 1-626 


4-698 


579 


4-838 


534 


5-190 


1-432 


5-890 


1-264 


6-590 


J3 1 


4-420 1-676 


4-560 1-625 


4-700 


578 


4-840 


533 


5-200 


1-429 


5-900 


1-262 


6-600 


130 


4-422 1-675 


4-562 1-625 


4-702 


577 


4-842 


533 


5-210 


1-427 


5-910 


1-260 


6-610 


128 


4-424 1-674 


4-564 1-624 


4-704 


'577 


4-844 


532 


5-220 


1-424 


5-920 


1-258 


6-620 


127 


4-426 1-673 


4-566 1-623 


4-706 


576 


4-846 


532 


5-23 


1-421 


5-93 


1-256 


6-630 


125 


4-428 1-673 


4-568 1-623 


4.708 


576 


4-848 


531 


5-240 


1-418 


5*94 


1-254 


6-640 


123 


4-430 1-672 


4-570 1-622 


4-710 


575 


4-850 


53 


5-250 


1-416 


5-95 


1-252 


6-650 


122 


4-432 1-671 


4-572 1-621 


4-712 


574 


4-852 


53 


5-260 


i -4*3 


5-96o 


1-250 


6-660 


120 


4-434 1-671 


4-574 1-621 


4-7I4 


574 


4-854 


529 


5-270 


1-411 


5-97 


1-247 


6-670 


118 


4-436 1-670 


4-576 1-620 


4-716 


573 


4-856 


528 


5-280 


1-408 


5-98o 


i'245 


6-680 


II 7 


4-438 1-669 


4-578 1-619 


4-718 


572 


4-858 


528 


5-290 


i-45 


5-990 


1-243 


6-690 


'US 


4-440 1-668 


4-580 1-618 


4-720 


572 


4-860 


527 


5-30 


1-403 


6-000 


1-241 


6-700 


II 3 


4-442 1-668 


4-582 1-618 


4-722 


57 1 


4-862 


527 


5-3io 


1-400 


6-010 


1-239 


6-710 


112 


4-444 1-667 


4-584 1-617 


4-724 


57 


4.864 


526 


5-320 


1-398 


6-020 


1-237 


6-720 


110 


4-446 1-666 


4-586 1-616 


4-726 


57 


4-866 


525 


5-33 


T '395 


6-030 


i'235 


6-730 


108 


4-448 1-665 


4-588 1-616 


4-728 


569 


4-868 


525 


5-34 


1-392 


6-040 


1-233 


6-740 


107 


4-450 1-665 


4-590 1-615 


4-73 


568 


4-870 


524 


5-350 


1-390 


6-050 


1-231 


6-750 


105 


4-452 1-664 


4-592 1-614 


4-732 


568 


4-872 


524 


5-36o 


1-387 


6-060 


1-229 


6-760 


103 


4-454 1-663 


4-594 1-614 


4*734. 


567 


4-874 


523 


5-37 


1-385 


6-070 


1-227 


6-770 


102 


4-456 1-663 


4-596 1-613 


4-736 


566 


4-876 


522 


5-38o 


1-382 


6-080 


1-225 


6-780 


100 


4-458 1-662 


4-598 1-612 


4-738 


566 


4-878 


2-522 


5-390 


1-380 


6-090 


1-223 


6-790 


099 


4-460 1-661 


4-600 i -612 


4-740 


565 


4-880 


2-521 


5-400 


!'377 


6-100 


I-22I 


6-800 


097 


4-462 i -660 


4-602 1-611 


4-742 


565 


4-882 


2-521 


5'4 10 


!'375 


6-110 


I-2I9 


6-810 


095 


4-464 i -660 


4-604 1-610 


4-744 


564 


4-884 


2-520 


5-420 


1-372 


6-120 


I-2I7 


6-820 


094 


4-466 1-659 


4-606 1-610 


4-746 


563 


4-886 


2-520 


5H30 


1-370 


6-130 


I-2I5 


6-830 


092 


4-468 1-658 


4-608 1-609 


4-748 


563 


4-888 


2-519 


5H4 


1-367 


6-140 


I-2I3 


6-840 


091 


4-470 1-657 


4-610 1-608 


4-75 


562 


4-890 


2-518 


5-450 


1-365 


6-150 


I -2 1 1 


6-850 


089 


4-472 1-657 


4-612 1-608 


4-752 


56i 


4-892 


2-517 


5-460 


1-362 


6-160 


I-2IO 


6-860 


088 


4-474 1-656 


4-614 1-607 


4-754 


561 


4-894 


2-517 


5'47 


1-360 6-170 


I -208 


6-870 


086 


4-476 1-655 


4-616 i -606 


4-756 


1-560 


4-896 


2-516 


5-480 


1-357 6-1 80 


I -206 


6-880 


084 


4-478 1-655 


4-618 i -606 


4-758 


1-559 


4-898 


2-516 


5H90 


1 '355 6-190 


I-20 4 


6-890 


083 



151 
EX=MERIDIAN TABLE No. 1. 

Showing the Reduction at i min. from the Meridian corresponding to the A and B Corrections 
given on Pages 12 to 37 of this Work. 



A and B 
Cor. 


Reduc- 
tion. 


A and B 
Cor. 


Reduc- 
tion. 


AandB 
Cor. 


Reduc 
tion. 


A and B 
Cor. 


Reduc- 
tion. 


AandB 
Cor. 


Reduc- 
tion. 


A and B Reduc- 
Cor. tion. 


AandB 
Cor. 


Reduc- 
tion. 


6-90 


ro8i 


7 -6o 


983 


8'6o 


869 


i 
lO'OO 


748 


11-40 


657 


12-80 -585 


i 

14-20 


527 


6-91 


1-080 


7 -6l 


9 8l 


8-62 


867 


10-02 


747 


II'42 


655 


12*82 -584 


I4-22 


527 


6-Q2 


1-078 


7-62 


980 


8-64 


865 


IO-04 


'745 


11-44 


654 


I2-8 4 -583 


14-24 


526 


6-93 


1-077 


7-63 


979 


8-66 


863 


10-06 


'744 


11-46 


653 


12-86 -582 


14-26 


525 


6-94 


1-075 


7-64 


977 


8-68 


861 


10*08 


742 


11-48 


652 


12-88 -581 


14-28 


525 


6'95 


1-074 


7-65 


976 


8-70 


859 


io- 10 


741 


11-50 


651 


12-90 -581 


14-30 


524 


6-96 


1-072 


7-66 


"975 


8-72 


857 


IO'I2 


739 


11-52 


650 


12-92 -580 


14-32 


523 


6-97 


1-071 


7-67 


'974 


8-74 


855 


10-14 


738 


ii-54 


649 


12-94 '579 


I4-34 


522 


6-98 


1-069 


7-68 


972 


8-76 


853 


10-16 


736 


11-56 


648 


12-96 -578 


14-36 


522 


6-99 


i -068 


7-69 


971 


8-78 


852 


10-18 


'735 


11-58 


646 


12-98 -577 


I4-38 


521 


7-00 


1-066 


7-70 


970 


8-80 


'850 


I0'20 


'734 


1 1 -60 


645 


13-00 -576 


14-40 


520 


7'01 


1-065 


7-71 


969 


8-82 


848 


IO'22 


732 


11-62 


644 


13-02 -575 


14-42 


519 


7'02 


1-063 


772 


967 


8-84 


846 


10-24 


731 


11-64 


643 


13-04 '574 


14-44 


-519 


7"3 


1*062 


7*73 


966 


8-86 


844 


10-26 


729 


n-66 


642 


13-06 -573 


14-46 


5 l8 


7-04 


i -060 


7'74 


965 


8-88 


842 


10-28 


728 


u-68 


641 


13-08 *573 


14-48 


517 


7'5 


1-059 


7-75 


964 


8-90 


840 


10-30 


726 


11-70 


640 


13-10 -572 


I4-50 


-517 


7 - 06 


1-057 


7-76 


962 


8-92 


838 


10-32 


725 


11-72 


639 


13-12 -571 


14-60 


513 


7-07 


1-056 


7'77 


961 


8-94 


836 


10-34 


724 


11-74 


638 


13-14 -570 


14-70 


510 


7-08 


1-054 


7-78 


960 


8-96 


835 


10-36 


722 


11-76 


637 


13-16 -569 


14-80 


506 


7-09 


1-053 


7-79 


"959 


8-98 


833 


10-38 


721 


11-78 


636 


13-18 568 


14-90 


-503 


7-10 


1-051 


7-80 


958 


9-00 


831 


10-40 


720 


11-80 


634 


13-20 -567 


15-00 


'499 


7-11 


1-050 


7-81 


956 


9*02 


829 


10-42 


7 I8 


11-82 " 


633 


13-22 -566 


15-10 


-496 


7-12 


1-048 


7-82 


'955 


9-04 


827 


10-44 


717 


11-84 


632 


13-24 -566 


15-20 


'493 


7'i3 


1-047 


7-83 


'954 


9-06 


825 


10-46 


'7*5 


n-86 


631 


13-26 -565 


15-30 


490 


7-14 


I-0 45 


7-84 


953 


9-08 


824 


10-48 


714 


n-88 


630 


13-28 -564 


I5-40 


487 


yi5 


1-044 


7-85 


952 


9-10 


822 


10-50 


713 


11-90 


629 


13-30 -563 


I5-50 


483 


7-16 


1-042 


7-86 


950 


9-I2 


820 


10-52 


711 


11-92 


628 


13-32 -562 


15-60 


480 


7-17 


1-041 


7-87 


'949 


9-I4 


818 


10-54 


710 


11-94 


627 


I3-34 -561 


15-70 


'477 


7-18 


1-040 


7-88 


948 9-16 


816 


10-56 


709 


11-96 


626 


13-36 -561 


15-80 


"474 


7-19 


1-038 


7-89 


'947 


9-18 


815 


10-58 


707 


11-98 


625 


13-38 -560 


15-90 


471 


7-20 


1-037 


7-90 


946 


9*20 


813 


10-60 


706 


I2'00 


624 


13-40 559 


16-00 


468 


7-21 


1-035 


7-91 


'944 


9'22 


8n 


10-62 


705 


I2'02 


623 


13-42 -558 


16-10 


465 


7-22 


1-034 


7-92 


"943 


9-24 


809 


10-64 


'73 


I2'04 


622 


I3-44 '557 


16-20 


463 


7' 2 3 


1-032 


7"93 


942 


9-26 


808 


10-66 


702 


I2'O6 


621 


13-46 -556 


16-30 


460 


7-24 


1*031 


7'94 


941 


9-28 


806 


10-68 


701 


12-08 


620 


13-48 -556 


16-40 


457 


7-25 


1-030 


7-95 


940 


9-30 


804 


10*70 


699 


I2'IO 


619 


13-50 '555 


16-50 


"454 


7-26 


1-028 


7-96 


'939 


9-32 


802 


10-72 


698 


I2'I2 


618 


13*52 "554 


16-60 


451 


7-27 


1-027 


7-97 


'937 


9'34 


801 


10-74 


697 


I2'I 4 


617 


I3-54 '553 


16-70 


'449 


7-28 


1-025 


7-98 


936 


9'36 


799 


10-76 


696 


I2'l6 


616 


13-56 '552 


16-80 


446 


7-29 


1-024 


7-99 


'935 


9-38 


'797 


10-78 


694 


I2'l8 


615 


13-58 'SSI 


16-90 


"443 


7"3o 


1-023 


8-00 


'934 


9-40 


796 


10-80 


693 


I2'2O 


614 


13-60 -551 


17-00 


441 


7"3i 


I'O2I 


8-02 


932 


9-42 


'794 


10-82 


692 


I2'22 


613 


13-62 -550 


17-10 


438 


7-32 


I'O20 


8-04 


929 


9'44 


792 


10-84 


690 


I2'24 


612 


13-64 -549 


17-20 


436 


7'33 


I'OlS 


8-06 


927 


9- 4 6 


791 


10-86 


689 


12-26 


611 


13-66 -548 


17-30 


'433 


7"34 


1-OI7 


8-08 


925 


9-48 


789 


10-88 


688 


12-28 


610 


13-68 -548 


17-40 


431 


7"35 


1-016 


8-10 


922 


9 ! 50 


787 


10-90 


687 


12-30 


609 


13-70 547 


17-50 


428 


7-36 


1-014 


8-12 


920 


9-52 


786 


10-92 


685 


I2-32 


608 


13-72 -546 


17-60 


426 


7'37 


1-013 


8-14 


918 


9'54 


784 


10-94 


684 


I2 '34 


607 


I3-74 '545 


17-70 


423 


7-38 


1*012 


8-16 


916 


9-56 


78 1 


10-96 


683 


12-36 


606 


13-76 -544 


17-80 


421 


7'39 


I'OIO 


8-18 


913 


9-58 


781 


10-98 


682 


12-38 


605 


13-78 '543 


17-90 


419 


7-40 


1-009 


8-20 


911 


9-60 


779 


II'OO 


*68o 


12-40 


604 


13-80 -543 


18-00 


416 


7'4i 


1-008 


8-22 


909 


9-62 


778 


H'O2 


679 


12-42 


603 


13-82 -542 


18-10 


414 


7-42 


i -006 


8-2 4 


907 


9-64 


776 


II'O4 


678 


12-44 


602 


13-84 -541 


18-20 


412 


7H3 


1-005 


8-26 


905 


9-66 


'774 


1 1 'O6 


677 


12-46 


601 


13-86 -540 


18-30 


410 


7'44 


1-004 


8-28 


902 


9-68 


"773 


1 1 -08 


676 


12-48 


600 


13-88 -540 


18-40 


407 


7'45 


1-002 


8-30 


900 


9-70 


771 


II'IO 


674 


12-50 


'599 


13-90 *539 


18-50 


405 


7-46 


I'OOI 


8-32 


898 


9-72 


770 


11' 12 


673 


12-52 


598 


13-92 -538 


18-60 


403 


7-47 


999 


8-34 


896 


9'74 


768 


II'I4 


672 


12-54 


'597 


I3-94 '537 


18-70 


401 


7-48 


998 


8-36 


894 


9-76 


766 


H'i6 


671 


12-56 


596 


13-96 -536 


18-80 


'399 


7 '49 


997 


8' 3 5 


892 


9-78 


765 


11-18 


670 


12*58 


'595 


13-98 -536 


18-90 


'397 


7'5o 


996 


8-40 


890 


9-80 


763 


II'2O 


668 


I2'6o 


'594 


14*00 -535 


19-00 


'394 


7-5i 


994 


8-42 


888 


9-82 


762 


II'22 


667 


12-62 


'593 


14-02 -534 


19-10 


392 


7"52 


993 


8-44 


885 


9-84 


760 


11-24 


666 


12-64 


592 


14-04 '533 


19-20 


390 


7'53 


992 


8-46 


883 


9-86 


759 


11*26 


665 


12-66 


59i 


14-06 -533 


19-30 


388 


7"54 


990 


8-48 


881 


9-88 


'757 


11-28 


664 


12-68 


59i 


14-08 -532 


19-40 


386 


7-55 


989 


8-50 


879 


9-90 


756 


II*3O 


662 


12-70 


590 


14-10 -531 


19-50 


384 


7-56 


988 


8-52 


877 


9-92 


'754 


11*32 


661 


12-72 


589 


14-12 -530 


19-60 


382 


7*57 


986 


8-54 


875 


9'94 


'753 


n"34 


660 


12-74 


588 


14-14 -530 


19-70 


380 


7-58 


985 8-56 


873 


9-96 


'75 1 


11*36 


659 


12-76 


587 


14-16 -529 


19-80 


'379 


7-59 


984 8-58 


871 


9-98 


750 


11*38 


658 


12-78 


586 


14-18 -528 


2O "OO 


375 




j 



















152 

Table showing the Hour= angle Limits within which the Error of the Reduction 
calculated by Ex=meridian Table No. 2 will not exceed 0*5'. 



LATITUDE AND DECLINATION OF SAME NAME. 



DECLINATION. 



54 55 56 57 58 59 



7 2/ 

687 
66* 
63* 



6ol 



5 6l 

54* 

52* 

49* 

5* 



761 
75* 

75l 
74 / 



65! 
6ol 

59' 
59' 



M. 

86/ 
8 3 / 
8 3 / 
8 3 / 
8 3 / 



761 
74 / 
74* 
7*1 



58* 62* 
58* 6ol 

56* 58* 
52' i 54' 
49' ! 52' 
39/ 4 2 ' i 46' 



M. M. 

12377 
I02/ I26n 
lOgl 12277 
II 3 * | 12077 
IIO/ i II877 

108* ! 

I06/ II077, 

I04/ io8w 
94/ 10677 
85/ : 10277 

76* ioo/ 
72* 88* 

64* ! 7S/ 

65* 



51* 



54' 



M. 

n? 
nBg 
i4? 



nog] 99? 



io8g 
io6g 



97 g 
100 g 

I02g 

9877) 
94' 



I0 4? 
io 7 g 

io6g 

I02g 

9877 
94' 
77' 
661 



62 64 



93? 



87? 
84? 



8ig 



83* 



M. 

8ig 
Big 

77g 
77g 



79? 73? 
78? 73? 
77? 
76? 
75? 

75? 

74? 

74? 

72? 6gg 

7 ig 68g 

73? i 68g 



68 70 73 76 80 85 



M. 

8og 

77? 



73g 
73g 
7?g 
72? 



7ig 

68g 
68g 



M. 

8o< 



*5g 



75? 
73? 

. 



79? 

75? 
75? 
74? 



74?'! 
7? 
7? 
7? 



74.? 

73g 



6jg jog 



83s 
83^ 



8og 
79g 



M. 

02 
102^ 



lOIg 
lOIg 
101 g 
IQOg 

99g 
99g 



INFERIOR TRANSIT. 



NOTE. 

signifies that true re- 
duction is greater 
than tabular re- 
duction. 

signifies that true re- 
duction is less than 
tabular reduction 

signifies that there is 
no error as great as 
0-5' within limits of 
hour-angle which 
give A+ B greater 
than 3'ooo'. 



DECLINATION. 



68 70 ! 72 



M. 



ggg 

n8g io 4 g 



154' 

no/ i Sow 



M. 



100 g 
io6g 



74 C 



97g 



76 C 



M. 



78 80 C 

M. I'M. 



82 C 

M. 



94g 



94g 



92gi 

94? i 



IQOg lOOg 

io8je 104^ 



loog 

100 g 

104^ 



84 I 86 

_ j 

M 



M. 



I00g j 

ioog | 



I0 7 g 



M. 



lOOg j 10 

ioog 

I02g 
I3? 



104^ 

I06g II2g 



i3g 
i3g 



130? 



LATITUDE AND DECLINATION OF CONTRARY NAMES. 



o 



DECLINATION. 



54 55 56 57 . 58 59 



M. 
7 2/ 
701 

7 ol 
7 ol 
7 ol 

7 ol 
7 ol 
6gl 
6gl 

681 

681 
681 
681 
661 
65' 



77' 
77' 
77' 
7 6l 
7 6l 

75' 
75' 
73' 
73' 
73' 

7 2/ 
7 2/ 

6gl 

681 
681 
681 



861 

83' 
82 / 
82 / 
8o/ 

8o/ 
7 8/ 
7 6l 
75' 

75' 

74' 
73' 
72' 

7 2/ 

7 o/ 

70/ 



M. I M. 

12877. 
94/ I22/ 

93' 
go/ 
88/ 

861 

85' 

83' 

79' 

7 8/ 
77' 

75' 
73' 
72* 



io6/ 

97' 

9 2/ 

9 o/ 
8 7 / 
861 

8 4 / 

82 / 
8o/ 
7 8l 
7 6l 
7 6l 
7 6l 



140^ 

1427? 

I 4 2/ 

log/ 

I03/ 

g6l 

9 2/ 

gol 

881 
861 
8 4 / 
82 / 
80 / 
7 8/ 



M. 

nog 

I20g 



136? 
150? 

15477, 
i 3 i/ 
no/ 

I02/ 
981 

94' 
9o/ 

861 



8zl 



62 64 66 



102^ 

io8g 



92? 

9g 

ioog 



I20g 



nog- 



I62g 
I 7 877 

n6/ 

108* ! 14077 

ioo/ 



84? 
85? 



94? 
I0 4? 



I0 9? 



18 | 70 ' 73 

_ |_ ____ 



M. M. 

8og ! 7 8g 
8cg i 8ig 
8jg\ 8ig 



84? 
85? i 86g 

9og ; 90? 

95? 93? 
99? 94? 



M. 

78? 

Big 
Big 
Big 

82g 
82g 

85? 



76 80 85= 



M. | M. 
85? 



84? 
84? 

85? 



M. 
I02g 



153 
EX=MER!DIAN TABLE No. 2. 



Showing the Reduction at i min. from the Meridian corresponding to the 
given on Pages 12 to 37 of this Work. 


A and B Corrections 


A and B| Reduc- 
Cor. 1 don. 

j 


A and B 
Cor. 


Reduc- 
tion. 


A and B 
Cor. 


Reduc- 
tion. 


AandB 
Cor. 


Reduc- 
tion. 


A and B 
Cor. 


Reduc- 
tion. 


A and B 
Cor. 


Reduc- 
tion. 


A and B 
Cor. 

" 


Reduc- 
tion. 


t i 


f 


J t 


i 


/ 


t 


/ 


i 


/ 


t 






3*00 2*500 


370 


2-027 


4-40 


1-705 


5'10 


1-471 


5-80 


293 


6*50 


I-I54 


7-20 


1-042 


3-01 2-492 


371 


2'022 4-4! 


I'70I 


5'II 


1-468 


5-8i 


291 


6- 5 I 


I-I52 


7-21 


1-040 


3-02 2-483 


3-72 


2'0l6 


4-42 


1-697 


5-12 


I-465 


5-82 


289 


6- 5 2 


1-150 


7-22 


1-039 


3-03 2-475 


3'73 


2'OII 


4'43 


1-693 


5-I3 


1-462 


5-83 


286 


6-53 


1-148 


7-23 


1-037 


3-04 2-467 


3'74 


2-005 4-44 


1-689 


5-I4 


1-459 


5-84 


284 


6-54 


1-147 


7-24 


1-036 


3-05 2-459 


375 


2-000 4-45 


1-685 


5-I5 


1-456 


5-8 5 


282 


6-55 


I-I45 


7-25 


1-034 


3-06 2-451 


376 


i '995 


4-46 


1-682 


5'i6 


1-453 


5-86 


280 


6-56 


I M3 


7-26 


1-033 


3-07 2-443 


377 


1-989 


4-47 


1-678 


5'i7 


I-45I 


5-87 


2 7 8 


6-57 


1-142 


7-27 


1-032 


3-08 2-435 


378 


1-984 


4-48 


1-674 


5-i8 


1-448 


5-88 


2 7 6 


6-58 


1-140 


7-28 


1-030 


3-09 2-427 


379 


1-979 


4'49 


1-670 


5-i9 


i '445 


5-89 


273 


6-59 


1-138 


7-29 


1-029 


3-10 2-419 


3-80 


1-974 


4'5c 


1-667 


5-20 


1-442 


5'90 


271 


6-60 


1-136 


7-30 


1-027 


3-11 2-412 


3'8i 


1-969 


4'5i 


1-663 


5'2I 


1-440 


5'9i 


269 


6-61 


I-I35 


7-3I 


I-026 


3-12 2-404 


3-82 


1-963 


4*52 


1-659 


5'22 


i'437 


5'92 


267 


6-62 


I'I33 


7-32 


1-025 


3-13 2-396 


3-83 


1-958 


4*53 


1-655 


5-23 


i '434 


5-93 


265 


6-63 


1-131 


7'33 


1-023 


3-14 2-389 


3-84 


1-953 


4*54 


1-652 


5-24 


i-43i 


5-94 


263 


6-64 


1-130 


7'34 


I'022 


3-15 2-381 


3-85 


1-948 


4'55 


1-648 


5-25 


1-429 


5'95 


261 


6-65 


I-I28 


7'35 


1-020 


3'i6 2-373 


3-86 


1-943 


4-56 


I-645 


5-26 


1-426 


5-96 


2 5 8 


6-66 


I-I26 


7-36 


I'Oig 


3-17 2-366 


3-87 


1-938 


4'57 


1-641 


5-27 


1-423 


5-97 


2 5 6 


6-67 


1-124 


7-37 


I'OlS 


3-18 2-358 


3-88 


1-933 


4-58 


1-638 


5-28 


1*420 


5-98 


254 


6-68 


1-123 


7-38 


roi6 


3" r 9 2-351 


3-89 


1-928 


4'59 


1-634 


5-29 


1-418 


5'99 


252 


6-69 


I'I2I 


7'39 


1-015 


3-20 2-344 


3-90 


1-923 


4-60 


1-630 


5-30 


I-4I5 


6-00 


250 


6-70 


I-II9 


7-40 


1-014 


3-21 2-336 


3'9i 


1-918 


4-61 


1-627 


5-31 


1-412 


6-01 


248 


6-71 


1-118 


7-4i 


I'OI2 


3-22 2-329 


3-92 


1-913 


4-62 


1-623 


5-32 


1-410 


6-02 


246 


6-72 


rn6 


7-42 


I'OII 


3-23 2-322 


3'93 


1-908 


4-63 


1-620 


5'33 


1-407 


6*03 


"244 


6-73 


rn 4 


7'43 


1-009 


3'24 2-315 


3'94 


1-904 


4-64 


1-616 


5-34 


1-404 


6-04 


2 4 2 


6-74 


1-113 


7'44 


I -008 


3-25 2-308 


3'95 


1-899 


4' 6 5 


1-613 


5-35 


1-402 


6-05 


240 


6-75 


i-iii 


7'45 


1-007 


3-26 2-301 


3-96 


1-894 


4-66 


1-609 


5-36 


1-399 


6-06 


2 3 8 


6-76 


1-109 


7-46 


1-005 


3-27 2-294 


3'97 


1-889 


4-67 


i -606 


5'37 


i'397 


6-07 


2 3 6 


6-77 


1-108 


7-47 


1-004 


3-28 2-287 


3-98 


1-884 


4-68 


1-603 


5-38 


1-394 


6-08 


234 


6-78 


1-106 


7-48 


1-003 


3-29 2-280 


3'99 


I -880 


4-69 


1-599 


5-39 


1-391 


6*09 


232 


6-79 


1-105 


7-49 


I'OOI 


3-30 2-273 


4-00 


1-875 


4-70 


1-596 


5-40 


1-389 


6'io 


230 


6-80 


1-103 


7-50 


I'OOO 


3-31 2-266 


4-01 


1-870 


47i 


1-592 


5-4i 


1-386 


6-n 


227 


6-81 


I'lOI 


7'5i 


"999 


3-32 2-259 


4-02 


1-866 


4-72 


1-589 


5-42 


1-384 


6-12 


225 


6-82 


I -100 


7-52 


997 


3-33 2-252 


4-03 


1-861 


473 


1-586 


5-43 


1-381 


6-13 


223 


6-83 


1-098 


7-53 


996 


3-34 2-246 


4-04 


1-856 


4'74 


1-582 


5*44 


i '379 


6-14 


221 


6-84 


1-096 


7'54 


'995 


3'35 2-239 


4-05 


1-852 


4-75 


i '579 


5'45 


1-376 


6-15 


'220 


6-85 


1-095 


7-55 


"993 


3-36 2-232 


4-06 


1-847 


4-76 


1-576 


5H6 


J '374 


6-16 


218 


6-86 


1-093 


7-56 


992 


3-37 2-226 


4-07 


1-843 


4-77 


1-572 


5'47 


I-37 1 


6-17 


216 


687 


1-092 


7'57 


991 


3-38 2-219 


4-08 


1-838 


4-78 


1-569 


5-48 


1-369 


6-18 


214 


6-88 


1-090 


7-58 


989 


3-39 2-212 


4-09 


1-834 


4'79 


1-566 


5'49 


1-366 


6-19 


'212 


6-89 


1-089 


7-59 


988 


3-40 2'2O6 


4-10 


1-829 


4-80 


1-563 


5-50 


1-364 


6'2O 


210 


6-90 


1-087 


7-60 


987 


3-41 2-199 


4-11 


1-825 


4-81 


i"559 


5-5i 


1-361 


6-21 


208 


6-91 


1-085 


7-61 


986 


3- 4 2 2-193 


4-12 


1-820 


4-82 


1-556 


5-52 


1-359 


6-22 


206 


6-92 


1-084 


7-62 


984 


3-43 2-I87 


4'i3 


1-816 


4-83 


1-553 


5'53 


J '356 


6-2 3 


20 4 


6-93 


1-082 


7-63 


983 


3-44 2-180 


4-14 


1-812 


4-84 


i-55o 


5-54 


i'354 


6-2 4 


202 


6-94 


1-081 


7-64 


982 


3"45 2-174 


4^5 


1-807 


4-85 


1-546 


5-55 


i-35i 


6-25 


2OO 


6-95 


1-079 


7'65 


980 


3-46 2-168 


4-16 


1-803 


4-86 


1-543 


5-56 


1-349 


6-26 


I 9 8 


6-96 


1-078 


7-66 


'979 


3-47 2-161 


O7 


1-799 


4-87 


1-540 


5'57 


1-346 


6-27 


I 9 6 


6'97 


1-076 


7-67 


978 


3-48 2-155 


4-18 


1794 


4-88 


i"537 


5-58 


I- 344 


6-28 


194 


6-98 


1-074 


7-68 


'977 


3-49 2-149 


4-19 


1-790 


4-89 


1-534 


5'59 


1-342 


6-29 


192 


6'99 


1-073 


7-69 


'975 


3-50 2-143 


4-20 


1-786 


4-90 


i"53i 


5'6o 


1-339 


6-30 


190 


7-00 


1-071 


7-70 


"974 


3-5i 2-137 


4-21 


1-781 


4-91 


1-527 


5-6i 


1-337 


6-31 


I8 9 


7-01 


i -070 


7-71 


'973 


3-52 2-131 


4-22 


J 777 


4-92 


x "524 


5-62 


1-335 


6-32 


I8 7 


7-02 


1-068 


7-72 


972 


3'53 2-125 


4-23 


i'773 


4'93 


1-521 


5-63 


I-332 


6-33 


I8 5 


7-03 


1-067 


7-73 


970 


3-54 2-119 


4-24 


1-769 


4*94 


1-518 


5-64 


I-330 


6-34 


I8 3 


7-04 


1-065 


7'74 


969 


355 2-113 


4-25 


1-765 


4 '95 


I-5I5 


5-6 5 


1-327 


6-35 


181 


7'05 


1-064 


7-75 


968 


3-56 2-107 


4-26 


1-761 


4-96 


1-512 


5'66 


1-325 


6-36 


179 


7-06 


1-062 


7-76 


966 


3-57 2-101 


4-27 


1-756 


4'97 


1-509 


5-67 


1-323 


6-37 


177 


7-07 


1-061 


7'77 


965 


3-58 2-095 


4-28 


1752 


4-98 


1-506 


5-68 


1-320 


6-38 


176 


7-08 


1-059 


7-78 


964 


3-59 2-089 


4-29 


1-748 


4 "99 


i '503 


5-69 


1-318 


6-39 


*74 


7-09 


1-058 


7'79 


963 


3-60 2-083 


4-30 


1*744 


5-00 


1-500 


5-7o 


1*316 


6-40 


172 


7-10 


1-056 


7-80 


962 


3-61 2-078 


4'3i 


1-740 


5-01 


1-497 


57 1 


1-313 


6-41 


170 


7-11 


1-055 


7-81 


960 


3-62 2-072 


4-32 


1-736 


5-02 


1-494 


572 


1-311 


6-42 


1 68 


7-12 


1-053 


7-82 


959 


3-63 2-066 


4'33 


1-732 


5-03 


1-491 


573 


1-309 


6-43 


1 66 


7-I3 


1-052 


7-83 


958 


3-64 2-060 


4*34 


1-728 


5-04 


1-488 


5-74 


1-307 


6'44 


165 


7*14 


1-050 


7-84 


'957 


3-65 2-055 


4*35 


1-724 


5-05 


1-485 


5-75 


1-304 


6-45 


163 


7 >J 5 


1-049 


7-85 


'955 


3-66 2-049 


4'36 


1-720 


5-06 


1-482 


5-76 


1-302 


6-46 


161 


7-16 


1-047 


7-86 


"954 


3-67 2-044 


4'37 


1-716 


5-07 


1-479 


5*77 


1-300 


6-47 


159 


7-17 


1-046 7-87 


'953 


3-68 2-038 


4-38 


1-712 


5-o8 


1-476 


578 


1-298 


6-48 


I 57 


7-18 


1-045 7'88 


952 


3-69 2-033 


4'39 


1-708 


5-09 


r< 473 


5-79 


1-295 


6-49 


156 


7-19 


1-043 


7-89 


95i 



154 



EX-MERIDIAN TABLE No. 2. 

Showing the Reduction at i min. from the Meridian corresponding to the A and B Corrections 
given on Pages 12 to 37 of this Work. 



AandB 
Cor. 


Reduc- 
tion. 


AandB 
Cor. 


Reduc- A and B Reduc- 
tion. Cor. ! tion. 


A and B 
Cor. 


Reduc- 
tion 


A and B 
Cor. 


Reduc- 
tion, 


AandB 
Cor. 


Reduc- A and B 
tion. Cor. 


Reduc- 
tion. 


7-90 


/ 
949 


8-60 


8 7 2 


9-30 -806 


IO-OO 


75 


10-70 


701 


11-40 


658 


12-20 


615 


7-91 


948 


8-61 


8 7 I 


9-31 -806 


10-01 


749 


10-71 


700 


II- 4 I 


657 


12-22 


614 


7-92 


947 


8-62 


870 


9-32 -805 


IO-O2 


749 


10-72 


7 00 


II- 4 2 


657 


I2-24 


61} 


7'93 


946 


8-63 


869 


9'33 '804 


IO-O3 


748 


10-73 


699 


11 '43 


656 


12-26 


612 


7'94 


945 


8-64 


868 


9-34 -803 


10-04 


747 


10-74 


698 


11-44 


656 


12-28 


611 


7-95 


943 


8-65 


867 


9-35 -802 


IO-O5 


746 


10-75 


698 


11 '45 


655 


12-30 


610 


7-90 


942 


8-66 


866 


9-36 -801 


10-06 


746 


10-76 


697 


11-46 


654 


I2-32 


609 


7'97 


941 


8-67 


865 


9-37 -800 


10-07 


745 


10-77 


696 


11-47 


654 


12-34 


608 


7-98 


94 


8-68 


864 


9-38 -800 


10-08 


'744 


10-78 


696 


11-48 


653 


12-36 


607 


7'99 


939 


8-69 


863 


9-39 -799 


10-09 


7'43 


10-79 


695 


11-49 


653 


12-38 


606 


8-00 


938 


8-70 


862 


9-40 -798 


IO-IO 


743 


10-80 


694 


1 1 '5 


6 5 2 


12-40 


605 


8-01 


936 


8-71 


861 


9-41 -797 


10-11 


742 


10-81 


694 


11-51 


6 5 2 


12-42 


604 


8-02 


935 


8-72 


860 


9-42 -796 


10-12 


741 


10-82 


693 


11-52 


6 5 I 


12-44 


603 


8-03 


934 


8-73 


8 5 9 


9H3 '795 


10-13 


740 


10-83 


6 93 


n-53 


6 5 


12-46 


602 


8-04 


933 


8-74 


858 


9'44 '794 


10-14 


-740 


10-84 


692 


n-54 


-6 5 


12-48 


601 


8-05 


932 


8-75 


857 


9'45 -794 


10-15 


739 


10-85 


691 


1 1 '55 


649 


12-50 


600 


8-06 


93 1 


8-76 


856 


9-46 -793 


10-16 


738 


10-86 


691 j 11-56 


6 4 9 


12-52 


'599 


8-07 


929 


8-77 


855 


9-47 -792 


10-17 


737 


10-87 


690 11-57 


648 


J 2'54 


598 


8-08 


928 


8-78 


854 


9-48 -791 


10-18 


737 


10-88 


689 11-58 


648 


12-56 


'597 


8-09 


927 


8-79 


853 


9-49 -790 


10-19 


736 


10-89 


689 


n-59 


6 47 


12-58 


596 


8-10 


926 


8-80 


852 


9-50 -789 


10-20 


'735 


10-90 


688 


1 1 -60 


6 47 


12-60 


595 


8-n 


925 


8-81 


851 


9-51 -789 


10-21 


735 


10-91 


687 


11-61 


646 


12-62 


'594 


8-12 


924 


8-82 


850 


9-52 -788 


10-22 


734 


10-92 


687 


11-62 


645 


12-64 


593 


8-13 


923 


8-83 


849 


9'53 -787 


IO-23 


733 


10-93 


686 


11-63 


645 


12-66 


592 


8-14 


921 


8-84 


848 


9-54 -786 


10-24 


732 


10-94 


686 


11-64 


644 


12-68 


591 


8-15 


920 


8-85 


847 


9'55 -785 


10-25 


732 


10-95 


685 


11-65 


644 


12-70 


59i 


8-16 


919 


8-86 


847 


9-56 -785 


10-26 


731 


10-96 


684 


n-66 


643 


12-72 


590 


8-17 


918 


8-87 


846 


9'57 -784 


10-27 


73 


10-97 


684 


11-67 


6 4 3 


12-74 


589 


8-18 


917 


8-88 


845 


9-58 -783 


10-28 


730 


10-98 


683 


n-68 


6 4 2 


12-76 


588 


8-19 


916 


8-89 


844 


9-59 -782 


10-29 


729 


10-99 


682 


11-69 


642 


12-78 


587 


8-20 


915 


8-90 


8 43 


9-60 -781 


10-30 


728 


11-00 


682 11-70 


6 4 I 


12-80 


586 


8-21 


9M 


8-91 


842 


9-61 -780 


10-31 


727 


1 1 -01 


681 


11-71 


640 


12-82 


585 


8-22 


912 


8-92 


841 


9-62 -780 


10-32 


727 


1 1 -02 


681 


11-72 


640 


12-84 


584 


8-2 3 


911 


8-93 


840 


9-63 -779 


I0 '33 


726 


I -03 


680 


11 -73 


039 


12-86 


583 


8-2 4 


910 


8-94 


839 


9-64 -778 


10-34 


725 


I -04 


679 


11-74 


639 


12-88 


582 


8-2 5 


909 


8-95 


838 


9-65 -777 


iQ-35 


725 


I -05 


679 


n-75 


638 


12-90 


581 


8-26 


908 


8-96 


837 


9-66 -776 


10-36 


724 


I -06 


678 


11-76 


6 3 8 


12-92 


580 


8-27 


907 


8-97 


836 


9-67 -776 


10-37 


723 


I -07 


678 


11-77 


637 


12-94 


580 


8-28 


906 


8-98 


835 


9-68 -775 


10-38 


723 


08 


677 


11-78 


637 


12-96 


579 


8-29 


905 


8-99 


834 


9-69 '774 


10-39 


722 


09 


676 


11-79 


636 


12-98 


578 


8-30 


904 


9-00 


833 


9-70 -773 


10-40 


721 


10 


676 


11-80 


636 


13-00 


577 


8-31 


903 


9-01 


832 


9-71 -772 


10-41 


720 


II 


675 


11-81 


635 


13-02 


576 


8-32 


-901 


9-02 


831 


9-72 -772 


10-42 


720 


12 


674 


11-82 


635 


13-04 


575 


8'33 


900 


9-03 


831 


9'73 '77 1 


10-43 


719 


13 


674 


11-83 


634 


13-06 


574 


8-34 


899 


9-04 


830 


9'74 '77 


10-44 


718 


-I 4 


673 


11-84 


633 


13-08 


573 


8-35 


898 


05 


829 


9'75 -769 


10-45 


718 


15 


673 


11-85 


633 


13-10 


'573 


8-36 


897 


06 


828 


9-76 -768 


10-46 


717 


16 


672 


n-86 


6 3 2 


3-12 


572 


8-37 


896 


07 


827 


9-77 -768 


10-47 


716 


17 


671 


11-87 


6 3 2 


3-14 


57 1 


8-38 


895 


08 


826 


9-78 -767 


10-48 


716 


18 


671 


n-88 


-6 3 I 


3-16 


570 


8-39 


894 


09 


825 


9-79 -766 


10-49 


715 


19 


670 


11-89 


6 3 I 


3-18 


569 


8-40 


893 


10 


824 


9-80 -765 


10-50 


714 


20 


670 


11-90 


630 


3-20 


568 


8-41 


892 


II 


823 


9-81 -765 


10-51 


-714 


21 


669 


11-91 


630 


3-22 


567 


8-42 


891 


12 


822 


9-82 -764 


10-52 


713 


22 


668 


11-92 


629 


3-24 


566 


8-43 


890 


13 


821 


9-83 -763 


10-53 


712 


23 


668 


n-93 


629 


3-26 


566 


8-44 


889 


I 4 


821 


9-84 -762 


io-54 


712 


24 


667 


11-94 


628 


3-28 


565 


8'45 


888 


15 


820 


9-85 -761 


10-55 


711 


25 


667 


n-95 


628 


3-30 


564 


8-46 


887 


16 


819 


9-86 -761 


10-56 


710 


26 


666 


11-96 


627 


3-32 


563 


8'47 


885 


17 


818 


9-87 -760 


10-57 


710 


27 


665 


11-97 


627 


3'34 


562 


8-48 


884 


18 


817 


9-88 -759 


10-58 


-709 


28 


665 


11-98 


626 


3-36 


561 


8-49 


88} 


19 


816 


9-89 -758 


10-59 


708 


29 


664 


11-99 


626 


3-38 


561 


8-50 


882 


20 


815 


9-90 -758 


1 0-60 


708 


3 


664 


12-00 


625 


3-4 


560 


8-51 


881 


9-21 


814 


9-91 -757 


10-61 


77 


31 


663 


12-02 


624 


3H2 


559 


8-52 


880 


9-22 


813 


9-92 -756 


10-62 


706 


32 


66 ? 


I2-04 


-623 


3-44 


558 


8-53 


879 


9-23 


813 


9'93 '755 


10-63 


706 


33 


662 


12-06 


622 


3-46 


557 


8-54 


878 


9-2 4 


812 


9'94 '755 


10-64 


75 


34 


661 


12-08 


621 


3-48 


556 


8-55 


877 


9-25 


811 


9-95 '754 


10-65 


704 


35 


661 


12-10 


620 


3'5 


556 


8-56 


876 


9-26 


810 


9-96 -753 


10-66 


704 


36 


660 


12-12 


619 


3-52 


555 


8-57 


875 


9-27 


809 


9-97 -752 


0-67 


70 


37 


660 


12-14 


618 


3'54 


554 


8-58 


874 


9-28 


808 


9-98 -752 


10-68 


702 


38 


659 


I2-I6 


617 


3-56 


553 


8'59 


873 | 9-29 


807 


9-99 -751 


0-69 


702 


39 


658 12-18 


616 


3-58 


552 



155 
EX=MERIDIAN TABLE No. 2. 

Showing the Reduction at i min. from the Meridian corresponding to the A and B Corrections 

given on Pages 12 to 37 of this Work. 



A and B 
Cor. 


Reduc- 
tion. 


A andB 
Cor. 


Reduc- 
tion. 


A and B 
Cor. 


Reduc- 
tion. 


A and B Reduc- 
Cor. i tion. 

i 


A andB 
Cor. 


Reduc- 
tion. 


A andB 
Cor. 


Reduc- 
tion. 


A and B 
Cor. 


Reduc- 
tion. 


13-60 


55* 


17-10 


439 


20-6o 


364 


/ / 
24-5 '36 


3I-50 


238 


45-20 


166 


77-0 


097 


I3-65 


549 


!7'i5 


437 


20-65 


363 


24-60 -305 


31-60 


237 


45-4 


-165 


78-0 


-096 


13-70 


'547 


17-20 


436 


20-70 


362 


24-70 -304 


31-70 


237 


45-60 


165 


79-0 


95 


13-75 


545 


i7'25 


435 


20-75 


361 


24-80 -302 


31-80 


236 


45-8o 


164 


80-0 


094 


13-80 


543 


17-30 


434 


20-80 


- 3 6I 


24-90 -301 


32-00 


234 


46-00 


-163 


81-0 


093 


I3-85 


542 


*7'35 


432 


20-85 


360 


25-00 -300 


32-20 


233 


46-20 


162 


82-0 


091 


13-90 


54 


17-40 


'43 1 


20-90 


359 


25-10 -299 


32-40 


232 


46-40 


162 


83-0 


-090 


13-95 


538 


!7'45 


430 


20-95 


358 


25-20 -298 


32-60 


23 


46-60 


161 


84-0 


089 


14-00 


536 


17-50 


429 


21-00 


357 


25-30 -296 


32-80 


229 


46-80 


i 60 


85-0 


088 


14-05 


534 


17-55 


427 


21-05 


356 


25'4 '295 


33-oo 


227 


47-00 


i 60 


86-0 


-087 


14-10 


532 


17-60 


426 


2I-IO 


355 


25-50 -294 


33-20 


-226 


47-20 


159 


87-0 


-086 


I4-J5 


53 


17-65 


425 


21-15 


355 


25-60 -293 


33-4 


225 


47-40 


158 


88-0 


085 


14-20 


528 


17-70 


424 


21-20 


'354 


25.70 -292 


33-6o 


223 


47-60 


-158 


89-0 


084 


i4- 2 5 


526 


J 7-75 


423 


21-25 


353 


25-80 -291 


33-8o 


-222 


47-8o 


157 


90-0 


083 


I4-3 


524 


17-80 


421 


21-30 


352 


25-90 -290 


34-00 


221 


48-00 


-156 


91-0 


082 


I 4'35 


523 


17-85 


420 


2i'35 


35 1 


26-00 -289 


34'20 


219 


48-20 


156 


92-0 


082 


14.40 


-521 


17-90 


.419 


21-40 


351 


26-10 -287 


34-4 


218 


48-40 


155 


93-o 


-081 


M'45 


5i9 


17-95 


418 


21-45 


35 


26-20 -286 


34-6o 


217 


48-60 


154 


94-0 


080 


14-50 


517 


1 8 -oo 


-417 


21-50 


349 


26-30 -285 


34-8o 


216 


48-80 


!54 


95' 


079 


I4-55 


5i5 


18-05 


-416 


21-55 


348 


26-40 -284 


35-0 


214 


49-00 


153 


96-0 


078 


14-60 


5M 


18-10 


414 


21-60 


347 


26-50 -283 


35-20 


213 


49-20 


152 


97-0 


77 


i4- 6 5 


512 


18-15 


4J3 


21-65 


346 


26-60 -282 


35-4 


212 


49-4 


152 


98-0 


-077 


14-70 


510 


18-20 


412 


21-70 


346 


26-70 -281 


35-6o 


211 


49-60 


151 


99-0 


076 


14-75 


508 


18-25 


411 


21-75 


345 


26-80 -280 


35-8o 


210 


49-80 


151 


1 00-0 


75 


14-80 


57 


18-30 


410 


21-80 


344 


26-90 -279 


36-00 


-208 


50-00 


150 


IIO-O 


-068 


I4-85 


55 


18-35 


409 


21-85 


343 


27-00 -278 


36-20 


207 


50-20 


149 


I2O-0 


063 


14-90 


53 


18-40 


408 


21-90 


343 


27-10 -277 


36-4 


206 


50-40 


149 


1 30-0 


058 


I4-95 


502 


18-45 


47 


21-95 


342 


27-20 -276 


36-60 


205 


50-60 


148 


140-0 


54 


15-00 


500 


18-50 


45 


22-00 


34 1 


27-30 -275 


36-80 


204 


50-80 


-148 


I50-0 


050 


i5-5 


498 


18-55 


44 


22-05 


34 


27-40 -274 


37-00 


203 


51-00 


147 


I 6O-0 


47 


15-10 


497 


1 8-60 


43 


22-10 


'339 


27-50 -273 


37-20 


202 


51-20 


1.47 


170*0 


44 


I5-I5 


495 


18-65 


42 


22-15 


339 


27-60 -272 


37'4 


-201 


51-4 


-146 


I 80-0 


042 


15-20 


493 


18-70 


401 


22-20 


338 


27-70 -271 


37-60 


200 


51-60 


145 


1 9o'-o 


039 


15-25 


492 


18-75 


400 


22-25 


337 


27-80 -270 


37-8o 


198 


51-80 


i45 


200 -o 


038 


15-3 


490 


1 8-80 


399 


22-30 


336 


27-90 -269 


38-00 


197 


52-00 


.144 


2IO"-0 


036 


I5-35 


4 8 9 


18-85 


398 


22-35 


336 


28-00 -268 


38-20 


196 


52-20 


-144 


220-0 


034 


15-40 


487 


18-90 


397 


22-40 


335 


28-10 -267 


38-40 


195 


52-40 


143 


230-0 


33 


I5-45 


485 


18-95 


396 


22-45 


'334 


28-20 -266 


38-60 


194 


52-60 


i43 


240-0 


0.31 


15-5 


484 


19-00 


395 


22-50 


333 


28-30 -265 


38-80 


193 


52-80 


142 


250-0 


3 


15-55 


-482 


19-05 


394 


22-55 


333 


28-40 -264 


39-00 


192 


53-0 


142 


260-0 


029 


15-60 


-481 


19-10 


393 


22-60 


332 


28-50 -263 


39-20 


191 


53-20 


141 


270-0 


028 


15-65 


479 


19-15 


392 


22-65 


33 1 


28-60 -262 


39-40 


190 


53'4 


140 


280-0 


027 


15-70 


478 


19-20 


391 


22-70 


33 


28-70 -261 


39-60 


189 


53'6o 


140 


290-0 


026 


I5-75 


476 


19-25 


'39 


22-75 


33 


28-80 -260 


39-80 


i 88 


53'8o 


139 


300-0 


025 


15-80 


475 


19-30 


389 


22-80 


329 


28-90 -260 


40-00 


i 88 


54-00 


139 


320-0 


023 


15-85 


473 


I9-35 


388 


22-85 


328 


29-00 -259 


40-20 


187 


54-4 


-138 


340-0 


022 


15-90 


472 


19-40 


387 


22-90 


328 


29-10 -258 


40-40 


i 86 


54-8o 


137 


360-0 


O2 1 


15-95 


470 


19-45 


386 


22-95 


327 


29-20 -257 


40-60 


185 


55-20 


136 


380-0 


020 


1 6-00 


469 


19-50 


385 


23-00 


326 


29-3 -256 


40-80 


184 


55-6o 


135 


400-0 


019 


16-05 


467 


19-55 


384 


23-05 


325 


29-40 -255 


41-00 


183 


56-00 


J34 


420-0 


018 


16-10 


466 


19-60 


383 


23-10 


325 


29-50 -254 


41-20 


182 


57-00 


132 


440-0 


017 


16-15 


464 


19-65 


382 


23-15 


324 


29-60 -253 


41-40 


181 


58-00 


129 


460-0 


016 


16-20 


463 


19-70 


-381 


23-20 


323 


29.70 -253 


41-60 


180 


59-00 


-127 


480-0 


016 


16-25 


-462 


I9-75 


380 


23-25 


323 


29-80 -252 


41-80 


179 


60 -oo 


125 


500-0 


015 


16-30 


-460 


19-80 


379 


23-30 


322 


29-90 -251 


42-00 


-179 


61-00 


-123 


520-0 


-014 


16-35 


459 


19-85 


378 


23-35 


321 


30-00 -250 


42-20 


178 


62-00 


121 


54-0 


014 


16-40 


457 


19-90 


377 


23-40 


-321 


30-10 -249 


42-40 


177 


63-00 


119 


560-0 


013 


16-45 


456 


19-95 


376 


23-45 


320 


30-20 -248 


42-60 


176 


64-00 


117 


580-0 


013 


16-50 


'455 


20-00 


375 


23-50 


319 


30-30 -248 


42-80 


175 


65-00 


i*5 


6OO-O 


013 


16-55 


'453 


20-05 


'374 


23'55 


319 


30-40 -247 


43-00 


174 


66-00 


114 


650-0 


012 


1 6-60 


H52 


20-10 


373 


23-60 


-318 


30-50 -246 


43-20 


174 


67-00 


-112 


700-0 


Oil 


16-65 


450 


20-I5 


372 


23-65 


317 


30-60 -245 


43-4 


173 


68-00 


no 


750-0 


010 


16-70 


449 


20-20 


37 1 


23-70 


3J7 


30-70 -244 


43'6o 


172 


69-00 


IO9 


8OO-O 


009 


16-75 


448 


20-25 


37 


23-80 


3i5 


30-80 -244 


43-8o 


-171 


70-00 


I0 7 


9OO-O 


008 


16-80 


H46 


20-30 


'37 


23.90 


3M 


30-90 -243 


44-00 


171 


71-00 


106 


[000-0 


008 


16-85 


445 


20-35 


369 


24-00 


3*3 


31-00 -242 


44-20 


170 


72-00 


-104 


L2OO-0 


006 


16-90 


'444 


20-40 


368 


24-10 


'3 11 


31-10 -241 


44-40 


169 


73' 


103 


[500-0 


-005 


16-95 


442 


20-45 


367 


24-20 


310 


31-20 -240 


44-60 


168 


74-00 


101 


2000-0 


004 


17-00 


441 


20-50 


366 


24.30 


39 


31-30 -240 


44-80 


-167 


75-00 


100 


J5OO-O 


-003 


17-05 


-440 


20*55 


365 


24.40 


-307 


Si -40 -239 


45-00 


167 


76-00 


099 3000-0 


003 



ii Azimuth. 



156 
TABLE M. 

ERROR IN LATITUDE DUE TO AN ERROR OF 4 SECONDS IN TIME OR I' OF LONGITUDE. 



Azimuth. 1 


LATITUDE. 





5 


10 


15 


18 


20 


22 


24 


26 28 


30 


32 


34 


36 


38 


40 
































2 


03 


03 


03 


03 


03 


03 -03 


03 


03 


3 


03 


03 -03 


03 


03 


3 


4 


07 


07 


07 


07 


07 


07 


06 1 -06 


06 


06 


06 


06 ! -06 


06 


06 


5 


6 


ii 


10 


10 


10 


10 


10 


10 -10 


09 -09 


09 


09 -09 


09 


08 


08 


8 


14 


!4 


14 


14 


13 


13 


13 


13 


13 -12 


12 


12 -12 


ii 


II 


ii 


10 


18 


18 


17 


17 


17 


17 -16 


16 


16 


16 


15 


15 -15 


14 


14 


14 


12 


21 


21 


21 


21 


20 


20 '2O 


19 


19 


19 


18 


18 -18 


17 


17 


16 


J 4 


25 


25 


25 


2 4 


2 4 


23 '23 


23 


22 


22 


22 


21 -21 


20 


20 


19 


16 


29 


29 


28 


28 


2 7 


27 -27 -26 


26 


25 


25 


2 4 -2 4 


23 


23 


22 


18 


32 


.32 -32 


31 


31 


31 


3! -30 


29 


29 


28 


28 -27 


26 


26 


25 


20 


36 


36 ! -36 


35 


35 


34 


34 


33 


33 


32 


32 


31 -3 


29 


29 


28 


21 


38 


38 


38 


37 


37 


36 


36 


35 


35 


34 


33 


33 -32 


31 


30 


29 


22 


4 


4 


4 


39 


38 


38 


37 


37 


36 


36 


35 


34 '33 


33 


32 


31 


23 


42 


42 


42 


41 


40 


40 


39 


39 


38 


37 


37 


36 -35 


34 


33 


33 


24 


45 


44 


44 


43 


42 


42 


41 


4i 


40 


39 


39 


38 ;37 


36 


35 


34 


25 


47 


46 


46 


45 


44 


44 


43 


43 


42 


41 


40 


40: -39 


38 


37 


36 


26 


49 


49 


48 


47 


46 


46 


45 


45 


44 


43 


42 


41 -40 


39 


38 


37 


27 


5i 


5i 


50 


49 


48 


48 


47 


47 


46 -45 


44 


43 H 2 


41 


40 


39 


28 


53 


53 


52 


5i 


5i 


50 


49 


49 


48 -47 


46 


45 i '44 


43 


42 


41 


29 


55 


55 


55 


54 


53 


52 


5i 


5i 


50 -49 


48 


47 j -46 


45 


44 


H 2 


30 


58 


58 


57 


56 


55 


54 


54 '53 


52 -51 


50 


49 ( -48 


47 


45 


'44 


31 


60 


60 


59 


58 


57 


56 


56 


55 


54 '53 


52 


5i 


50 


49 


47 


46 


32 


62 


62 


62 


60 


59 


59 


58 


57 


56 -55 


54 


53 


52 


5i 


49 


48 


33 


65 


65 


64 


63 


62 


61 


60 


'59 


58 -57 


56 


55 


54 


53 


5i 


50 


34 


67 


67 


66 


65 


64 


63 


63 


62 


61 -60 


58 


57 


56 


55 


53 


52 


35 


70 


70 


69 


68 


67 


66 


65 


64 


63 -62 


61 


59 


58 


57 


55 


54 


36 


73 


72 


72 


70 


69 


68 


67 


66 


65! -64 


63 


62 


60 


59 


57 


56 


37 


75 


75 


74 


73 


72 


71 


70 


69 


68 -67 


65 


64 


62 


61 


59 


58 


38 


78 


78 


77 


75 


74 


73 


72 


71 


70 -69 


68 


66 


65 


63 


62 


60 


39 


81 


84 


80 


78 


77 


76 


75 


'74 


73 -72 


70 


69 


67 


66 


64 


62 


40 


84 


84 


83 


81 


80 


79 


78 


77 


75 -74 


73 


71 


70 


68 


66 


64 


4i 


87 


87 


86 


84 


83 


82 


81 


79 


78 -77 


75 


74 


72 


70 


69 


-67 


42 


90 


90 


89 


87 


86 


8 5 


83 


82 -81 -79 


78 


76 


75 


73 


71 


69 


43 


93 


93 


92 


90 


89 


88 


86 


8 5 


84 -82 


81 


79 


77 


75 


73 


71 


44 


97 


96 


95 


93 


92 


91 


90 


88 


8 7 


85 


84 


82 


80 


78 


76 


74 


45 


I-OO 


I -00 


98 


97 


95 


94 


93 


91 


90 


88 


87 


85 


83 


81 


79 


77 


46 


1-05 


1-03 


1-02 


I-OO 


98 


97 


96 


95 


93 


91 


90 


88 


86 


84 


82 


79 


47 


1-07 


1-07 


I -06 


1-04 


1-02 


I-OI 


99 


98 


96 


95 


93 


91 


89 


87 


84 


82 


48 


I-II 


I'll 


1-09 


1-07 


1-06 


1-04 


1-03 


I'Ql 


I-OO 


98 


96 


94 


92 


90 


88 


85 


49 


I-I5 


M5 


I-I3 


I'll 


1-09 


1-08 


1-07 


1-05 


1-03 


i -02 


I-OO 


98 


95 


93 


91 


88 


50 


1-19 


1-19 


I-I7 


ImI 5 


IM3 


I-I2 


I-IO 


1-09 


1-07 


1-05 


1-03 


I'OI 


99 


96 


94 


91 


5i 


1-23 


1-23 


1-22 


1-19 


1-17 


1-16 


1-14 


I-I3 


I'll 


1-09 


1-07 


1-05 


L-O2 


I-OO 


97 


95 


52 


1-28 


1-28 


1-26 


1-24 


1-22 


1-20 


1-19 


I-I7 


I-I5 


1-13 


I'll 


1-09 


I -06 


1-04 


I'OI 


-98 


53 


i-33 


1-32 


I'3I 


1-28 


1-26 


1-25 


1-23 


I-2I 


1-19 


1-17 


1-15 i -i-3 


I-IO 


07 


1-05 


1-02 


54 


1-38 


1-38 


I- 3 6 


i-33 


I- 3 I 


1-29 


1-28 


1-26 


1-24 


1-22 


1-19 1-17 


I-I4 -II 


1-08 


I-0 5 


55 


i-43 


1-42 


I- 4 I 


1-38 


I-36 


i-34 


i-32 


I- 3 


1-28 


1-26 


1-24 I-2I 


1-18 -16 


i-i3 


1-09 


56 


1-48 


1-48 


1-46 


!'43 


I-4I 


i'39 


i'37 


i-35 


i-33 


I-3I 


1-28 1-26 1-23 -20 


1-17 


I?X 1 


57 


i'54 


i'53 


1-52 


1-49 


I- 4 6 


i'45 


i-43 


1-41 


1-38 


I- 3 6 


i-33 i-3i 


1-28 -25 


I-2I 


i-i8 


58 


1-60 


i-59 


1-58 


1-55 


1-52 


1-50 


1-48 


1-46 


1-44 


I- 4 I 


1-39 1-36 


1-33 -29 


1-26 


1-23 


59 


1-66 


1-66 


1-64 


1-61 


I- 5 8 


1-56 


i'54 


1-52 


1-50 


1-47 


1-44 I-4 1 


1-38 -35 


I-3I 


1-27 


60 


i-73 


i-73 


I-7I 


1-67 


1-65 


1-63 


1-61 


1-58 1-56 


i'53 


1-50 1-47 


1-44 -40 


1-36 


i-33 


61 


1-80 


1-80 


I- 7 8 


1-74 


1-72 


1-71 


1-67 


1-65 1-62 


i-59 


i-56 i-53 


1-50 -46 


I- 4 2 


1-38 


62 


1-88 


1-87 


I-8 5 


1-82 


1-79 


1-77 1-74 


1-72 1-69 


1-66 


1-63 1-59 


i-56 -52 


1-48 1-44 


63 


1-96 


i-95 


i-93 


1-90 


1-8 


1-84, 1-82 


1-79 1-76 


!'73 


1-70 1-66 


1-63 -59 


i-55 i-5o 


64 


2-05 


2-04 


2-02 


1-98 


1-9 


1-93 | 1-90 


1-87! 1-84 


i-8i 


1-78 1-74 


1-70 


66 


1-62 


i-57 


65 


2-14 


2-14 


2-II 


2-07 


2-O, 


2-02 I'99 


1-96 


i-93 


1-89 


1-86 1-82 


1-78 


74 


1-69 


i 64 


66 


2-25 


2-24 


2'2I 


2-17 


2'I<: 


2-II 


2-08 


2-05 


2-02 


1-98 


1-95 1-90 


1-86 


82 


1-77 


1-72 


67 


2-36 


2-35 


2- 3 2 


2-28 


2'2; 


2-21 


2-18 


2-15 


2-12 


2-08 


2-04 2-00 1-95 


91 


1-86 


1-80 


68 


2-48 


2-47 


2'44 


2'39 


2-3 


2'33 


2-30 


2'26 2'22 


2-19 


2-14 2-10 2-05 


2'OO 


i-95 


1-90 


69 


2-61 


2-59 


2-57 2-52 


2'4 


2'45 


2-42 


2-38 2'34 


2-30 


2-26 2'2I 2'l6 


2'II 


2-05 


2-00 


70 


2'75 


2'74 


2.71 2-65 


2-6 


2-58 2-55 


2-51 2-47 


2'4 


2-38 2'33 2-28 2-22 


2'l6 2-10 



157 
TABLE M. 

?:RROR IN LATITUDE DUE TO AN ERROR OF 4 SECONDS IN TIME OR 1' OF LONGITUDE. 



Azimuth. 


LATITUDES 


42 


44 


46 48 


49 


50 51 


52 


53 


54 


55 


56 


57 58 


59 


60 












i 












o 
2 


03 


03 


02 


02 


02 


O2 i 'O2 -02 


02 


02 


02 


O2 '02 'O2 


02 


02 


4 


05 


05 


5 


05 


05 


04 i -04 '04 


4 


4 


4 


04 


04 -04 


4 


03 


6 


08 


08 


07 


07 


07 


07 -07 -06 


06 1 -06 


06 


06 


06 


06 


05 


05 


8 


10 


10 


10 


09 


09 


09 -09 | -09 


08 -08 


08 


08 


08 


07 


07 


07 


10 


13 


13 


12 


12 


12 


II -II -II 


II 


10 


10 


10 


10 


09 


09 


09 


12 


16 


15 


-I 5 


I 4 


I 4 


14 'IS 'IS 


13 


12 


12 


12 


12 


ii 


II 


II 


T 4 


19 


18 


17 


17 


16 


16 -16 -15 


15 


15 


14 


M 


M 


13 


13 


12 


16 


21 


21 


20 -19 


19 


18 -18 -18 


I 7 


I 7 


16 


16 


16 


15 


15 


J 4 


1.8 


24 


23 


23 


22 


21 


21 '2O '2O 


20 


19 


19 


18 


18 


17 


17 


16 


20 


27 


26 


25 


24 


24 


23 j -23 '22 


22 


21 


21 


20 


20 


19 


19 


18 


21 


29 


28 


27 


26 


25 


25 


24 -24 


23 


23 


22 


21 


21 


20 


20 


19 


22 


30 


29 


28 


27 


27 


26 


25 -25 


24 


24 


23 


23 


22 '21 


21 


20 


23 


32 


31 


29 


28 


28 


27 


27 -26 


26 


25 


24 


2 4 


23 


22 


22 


21 


2 4 


'33 


32 


31 


3 


29 


29 


28 -27 


27 


26 


26 


25 


2 4 


24 


23 


22 


25 


35 


34 


32 


31 


31 


3 


29 


29 


28 


27 


2 7 


26 


25 


25 


2 4 


23 


26 


36 


35 


34 


33 


32 


31 


3i 


30 


29 


29 


28 


27 


27 


26 


25 


2 4 


27 


38 


37 


35 


34 


33 


33 


32 


3i 


31 


3 


29 


28 


28 


2 7 


26 


25 


28 


40 


38 


37; -36 


35 


34 


33 


33 


32 


31 


3 


3 


29 


28 


27 


27 


29 


'4 1 


40 


39 '37 


36 


36 


'35 


34 


33 


33 


32 


31 


3 -29 


29 


28 


30 


'43 


42 


40 -39 


38 


'37 


36 -36 


35 


34 


33 


32 


3 I ! - 3 I 


3 


29 


31 


'45 


'43 


H 2 


40 


39 


39 


38 -37 


36 


'35 


'34 


34 


'33 


32 


31 


30 


32 


46 


'45 


43 


H 2 


4i 


40 


39 -38 


38 


'37 


36 


35 


'34 


33 


32 


31 


33 


48 


47 


45 


43 


43 


42 


41 -40 


39 


38 


'37 


36 


*35 


34 


33 


32 


34 


50 


49 


47 


45 


44 


'43 


42 -42 -41 


40 


39 


38 


37 


36 


'35 


34 


35 


52 


50 


49 


47 


46 


45 


44 '43 H 2 


'4 1 


40 


39 


38 


37 


36 


35 


36 


54 


52 


50 


49 


48 


47 


46 -45 -44 


43 


H 2 


"4 1 


40 


39 


37 


36 


37 


56 


54 


52 


50 


49 


48 


47 -46: -45 


'44 


'43 


42 


41 


40 


39 


38 


38 


58 


56 


'54 


52 


5i 


50 


49 -48 


47 


46 


45 


*44 


'43 


4i 


40 


39 


39 


60 


58 


56 


54 


53 


52 


5i i '50 


49 


48 


46 


'45 


'44 


43 


H 2 


40 


4 


62 -60 


58 


56 


55 


'54 '53 -52 


5i 


'49 


48 


'47 


46 


'44 


'43 


42 


4i 


6 5 


63 


60 


58 


57 


56 


55 '54 


52 


5i 


50 


49 


47 "46 


45 


'43 


4 2 


67 


6 5 


63 


60 


59 


58 


'57 '55 


'54 


'53 


52 


50 


'49 


4 


' 4 * 


45 


43 


69 


67 


65 


62 


61 


60 


59 '57 


56 


55 


53 


52 


5i 


49 


48 


47 


44 


72 


69 


67 


65 


63 


62 -61 -59 


58 


57 


55 


'54 


53 -51 


50 


48 


45 


'74 


72 


69 


67 


66 


64 -63 -62 


60 


59 


57 


56 


"54 


'53 


52 


50 


46 


'77 


74 


72 


69 


68 


67 i -65 -64 


62 


61 


59 


58 


56 


55 


'53 


52 


47 


80 


'77 


'74 


72 


70 


69 [ -67 -66 -65 


63 


62 


60 


58 


'57 


55 


'54 


48 


83 


80 


'77 


'74 


'73 


71 : -70 -68 


67 


6 5 


64 


62 


60 


'59 


57 


56 


49 


85 


83 


80 


'77 


'75 


74 -72 -71 


69 


68 


66 


64 


63 


61 


59 


58 


50 


89 


86 


83 


80 


78 


77 '75 


73 


72 


70 


68 


67 


6 5 


63 


61 


60 


5i 


92 


89 


86 


83 


81 


79 


78 


76 


'74 


73 


71 


69 


67 


65 


64 


62 


52 


'95 


92 


89 


86 


84 


82 


81 


79 


77 


75 


'73 


72 


70 


68 


66 


64 


53 


99 


'95 


92 


89 


87 


85 


84 


82 


80 


78 


76 


74 


72 


70 


68 


66 


54 


i -02 


99 


96 


92 


90 


88 


87 


8 5 


83 


81 


79 


77 


75 


73 


71 


69 


55 


i -06 


1-03 


99 


96 


94 


92 


90 


88 


86 


84 


82 


80 


78 


76 


74 


71 


56 


I'lO 


07 


1-03 


99 


97 


95 


93 *9i 


89 


87 


8 5 


83 


81 


'79 


76 


74 


57 


1-14 


ii 


1-07 


1-03 


01 


'99 '97 


95 


93 


91 


88 


86 


84 


82 


79 


77 


58 


1-19 


15 i-ii 


1-07 


05 


1-03 


I'OI 


99 


96 


94 


92 


89 


87 


85 


82 


80 


59 


1-24 


20 


1-16 


I'll 


09 


1-07 


05 1-02 


I'OO 


98 


95 


93 


91 


88 


86 


83 


60 


1-29 


25 


I'20 


1-16 


J 4 


i-ii 


09 1-07 


1-04 


1-02 


99 


97 '94 


92 


89 


87 


61 


i'34 


30 


1-25 


I-2I 


18 


16 


M 


ii 


09 


I -06 


05 


01 


98 


96 


93 


90 


62 


1-40 


35 


I' 3 I 


1-26 


23 


21 


18 


16 


13 


I-II 


08 


05 


02 


oo 


97 


'94 


63 


1-46 


'4 1 


I- 3 6 


1-31 


29 


26 


24 


21 


18 


I-I5 


13 


10 


07 


04 


I'OI 


98 


64 


1-52 


*47 


I-42 


i'37 


'34 


32 


29 


26 


23 


I'2I 


18 


15 


12 


09 


1-06 


1-03 


65 


i'59 


'54 


1-49 


i'43 


4i 


38 


35 


32 


29 


1-26 


23 


20 


17 


M 


I'lO 


1-07 


66 


1-67 


1-62 


1-56 


1-50 


"47 


"44 


Hi 


38 


'35 


32 


29 


26 


22 


19 


1-16 


I'I2 


67 


i'75 


1-69 


1-64 


1-58 


55 


51 


48 


45 


42 


38 


35 


32 


28 


25 


I'2I 


i-i8 


68 


1-84 


1-78 


1-72 


1-66 


62 


59 


56 


52 


49 


45 


42 


38 


'35 


'3 1 


I'2 7 


1-24 


69 


1-94 


1-87 


1-81 


i'74 


71 


67 


64 


60 


'57 


53 


49 


46 


42 


38 


i'34 


1-30 


70 


2-04 


1-98 


1-91 


1-84 


80 


77 


73 '69 


65 


61 


58 


54 


50 


46 


1-41 


i'37 



158 



POSITION OF SHIP FROM TWO SUN EX-MERIDIAN OBSERVATIONS, USING 
A AND B EX-MERIDIAN TABLES AND LOGARITHMS. 

1917. On January 2ist, a.m. at ship, in lat. by D.R. 8 o' N. and long. 74 22' E., when a 
chronometer indicated M.T. Green. 20 d. 17 h. 33 m. 51 s., the true altitude of sun's centre was 
52 34' S. ; and again on same afternoon when chronometer indicated 20 d. 21 h. i m. 21 s., the 
true altitude of sun's centre was 52 12" S., the ship having made 52 \ miles on a true N. 79 W. 
course during the interval between the observations. Required the position of ship at time of 
2nd observation, and prove work by two different methods. 



A.M. Observation. Latitude by Ex-meridian Tables. 



D. H. M. S. 

M.T. Green, 20 17 33 51 

Long. 74 22' E. + 4 57 28 

M.T. ship 22 31 19 

Eq. of time ii 19 

A.T. ship 22 20 o 

H.A. i 40 o 

Decl. 20 i\' 

Alt. 52 34' 

Azim. S. 40 47' E. gives A and 
B 1-17' which gives (p. 75) 
position-line S. 49 \ W., and 
(p. 145) Redn. at i m. 5'537' 
x 100 m. = Redn. 553-7, 
= 9 13-7'. 



Decl. (aist) 19 57 56 S. 
33-2" x 6-5 h. + 3 36 



Cor. dl. 



Sin. 9-8150 



Az. 40 47' 



M. s. . 

Eq. T. ii 23-4 

71 s. x 6-5 h. 4-6 



20 i 328. Cor. Eq. T. ii 18-8 



Run N. 79 W. 52^ = 10-0' N. 
51-5' W. = 52' W. 



Long. 
Run 



74 22-0 E. 
52-0 W. 



Long, at time of 73 30-0 E. 
2nd obsn. 



T. alt -0- 
Redii. 

Her. alt. 

M.Z.D. 
Decl. 

Lat. 
Run 



52 34'oS. 
- 9 13-7 

61 47-7 

28 12-3 N 

20 1-58. 

8 10-8 N. 

io-oN. 



Lat. at time of 8 20-8 N. 
2nd obsn. 



P.M. Observation. Ex-meridian Latitude by Spherical Calculation. 

D, H. M. S. M. S. 

M.T. Green. 2021 121 T. alt. -0- 52 12-0 S. Decl. (2ist) 1957568. Eq. T. (2ist) 1123-4 

Long. 73 30' E. + 4 54 o Var. 33-2" x 3 h. + i 40 Var. -71 s. x 3 h. 2-1 

Z.D. 37 48 N. 

M.T. ship 21 i 55 21 Cor. decl. 19 59 368. Cor. Eq. T. ii 21-3 



For Azimuth. 



A.T. ship (H.A.) 
Decl. 19 59' 36" S. 

Arc. (i) 22 2 1*8 S. 
Arc. (2) 29 52 14 N. 
Latitude 7 49 56 N. 



i 44 



Cot. 0-43909 
















Cot. 0-39375 


Alt. 52 12' 


Sec.' 0-21261 . . 


Cot. 9-88968 




Azim. 8.42 1 3' 5 2" W. 


Sin. 9-82745 


Cos. 9-86949 






Arc. (2) 29 52' 14" N. 


Tan. 9-75917 



As a Check on the Work the Ex-meridian Table No. i may be used. 

Lat. 7 50 N. \ A. -2825. 
Dl. 20 oS. [B. -8308. 
H.A. ih. 44m. f 

/ C. 1-1128. gives position-line N. 48 W. and redn. at i min. 5-753' x 104 m. 
^^ Redn. 598-3' = + 9 58-3' 



Z.D. 
Redn. 



M.Z.D. 
Decl. 



Latitude 



37 48-0 N. 
- 9 58-3 

27 49-7 N. 
19 59-6 S. 



Position on Chart. 

Lat. 8 5-8 N. 
Long. 73 I2-4E. 



7 50-1 N. 



With Long, at time of 2nd obsn. 73 30 E. 
Lat. (i) ,, 8 20-8 N. j" 

(2) 7 5o-o N. ) 



Gives position on Chart 

Lat. 8 s'-8 N. 
Long. 73 i2'2 E. 



159 



EXAMPLE FROM PREVIOUS PAGE WORKED FROM TWO LONGITUDE 

CALCULATIONS. 



A.M. Observation. 

\j. H. M. S. , 

M.T. Green. 20 17 33 51 True alt. -0- 52 348. 

Eq. time . n 19 o / // 

Decl. 20 i 328. 
A. T. Green. 20 17 22 32 i 



P.M. Observation. 

II. M. S. 

M.T. Green. 21 i 21 True alt. 52 i2'-oS. 

Eq. time u 21-3 

, ~ _ Decl. 19 59 3 f,S. 

A.I. Green. 20 49 59-7 ^^^^^ 



Run N. 79 W. 52^ m. = 10-0' N. 51-5' =52-0' W. 



A 52 34 o 
L 800 
P no i 32 


Sec. 0-00425 
Cosec. 0-02708 

Cos. 8-91384 
Sin. 9-73293 


-J 10' tO' 7330' 


'$/ ' 

< y*/ ^ 


170 35 32 


S 85 17 46 


S - A 32 43 46 




H.A. 

A.T. ship 
A.T. Green. 

Long, in time 

Longitude 
Run 


Sin.2 8-67810 


i 40 52 A -30 S. 
B 86 S 


22 19 8 

17 22 32 C2 1-16 S. gives posn.- 


4 56 36 W. 


74 9 o E. 
52 o W. 


Long, at time of 2nd obsn. 73 17 o E. 


P.M 

A 52 
L 8 
P 109 


, Observation. 

12 

10 o Sec. 0-00443 
59 36 Cosec. 0-02700 A.T. ship 


13" 10' 2O' 30' 


Position by chart Lat. 8 5*8 N. Long. 73 12*2' E. 

H. M. S. 
I 4 2 29-7 , 

20 49 59-7 A -30 S. 


170 

S 85 
S - A 32 


21 36 
Long, in tn 
10 48 Cos. 8-92441 
58 48 Sin. 9-73588 Longitude 


ne 4 52 30 E. 
C2 1-148. gives posn.-line 
73 7' 30" E. S. 48-7 E. 



H.A. ih. 42m. 29.73. 



Sin.2 8-69172 



Worked without the aid of Chart. 
Long, (i) 73 17-0 E. A & B 1-168. to W. 



(2) 


73 7-5 E. 


1-148. to E. 


Diff. long. 


9-5 


.:- 2-30 = Lat. Cor. 4-1'^ x 1-14' 
Long. Cor. 4-7' E. 


Lat. (2) 


8 io-oN. 


Long. (2) 


73 


7-5 E. 


Cor. 


4-1 S. 


Cor. 




4-7 E. 


P& 
Lat. in 


8 5-9 N. 


Long, in 


73? 


12-2 E. 



160 

Example from 2nd edition of "Calculated Hour-angles and Ex-meridian Tables," &c., by 
H. S. Blackburne, giving a true position from a right-angle cross of two sun observations less 
than 5 minutes from noon. 

POSITION FROM TWO EX-MERIDIAN OBSERVATIONS OF SUN WITH ALTITUDES 

LESS THAN 1J FROM ZENITH. 

1917- March igth, in approximate position in lat. o and long. 45 W., with the following 
observations find the position of ship at time of second observation : 

H. M. s. 

(A.M. at ship) M.T. Greenwich 3 2 51 T. alt. of -0- 88 41 S.Ed. 
(P.M. at ship) 3 9 27 88 47-4 S.Wd. 

Run in interval between observations West. i| miles. 



M.T. Green. 
Eq. time 



A.T. Green. 2 54 54 

Long. 44 58!' W. 2 59 54 



A.M. Observation. 

H. M. s. 

3 2 51 

- 7 57 



23 55 



A.T. Sp. 

H.A. o 5 o 

Alt. 88 41' 

Azim. S. 71 43' E. gives 
(P- 293) Redn. at i m. = 
10-835 s. X 5 m. = Redn. 
54-2'. 



Sin. 
Sec. 



1-6387 



T. alt. -9- 
Redn. 

Mer. alt. 

M.Z.D. 
Decl. 

Lat. 



88 41 S. 
+ 54-2 

89 35-2 

o 24-8 N. 
o 37-0 S. 



Sin. 9-9775 



Posn. on chart 



P.M. Observation. 



H. M. S. 

3 9 27 
- 7 57 



i 30 
00 



M.T. Green. 
Eq. time 

A.T. Green. 
Long. 45 W. 

H.A. West. 
Alt. 88 47-4' 



Azim. S. 1 8 3 ' W. gives 
Redn. at i m 2-38' x 
i m. = Redn. 3-6'. 



i 30 



T. alt. 
Redn. 



Mer. alt. 



M.Z.D. 
Decl. 



Lat. 



47-4 S. 
3-6 



88 51-0 

i 9-0 N. 
o 37-0 S. 

o 32-0 N. 



Sin. 7-8159 
Sec. 1-6754 



30' 



> 



Equator 




Equator 



"V50 W 5O 4O' 3O 

Parallel of Oecl. 0*37' S~ 



This example as 'an extreline case where both altitudes were near the zenith, and the D.R. 
position considerably in error illustrates clearly the errors which would result from considering 
the position-lines as straight lines; the resulting position being o 27-7' N. and 44 46-8' W. 
A perfectly true position, however, is obtained by the method here shown. 

On the meridian of 45 W. lat. (i) was found to be o 12-2' S. when sun bore S. 72 E. with 
Z.D. 79'. 

On the meridian of 45 W. lat. (2) was found to be o 32-0' N. when sun bore S. 18 W. with 
Z.D. 72-6'. 

In such an extreme case, if inconvenient to adopt this method, a second calculation could 
very quickly be made by the use of the ex-meridian table with a new hour-angle deduced from 
the approximate longitude obtained by the first calculation. When nearly under the sun the 
longitude is seldom likely to be much in error as the sun would be close to the prime vertical 
during almost the whole day. 



161 



DOUBLE PROOF OF CORRECTNESS OF POSITION AS DETERMINED 
METHOD AND CALCULATION OF PREVIOUS EXAMPLE. 



BY THE 



The following is a very good and simple way of proving the accuracy of double altitude 
observations, viz. : 

With the resulting longitude deduce a new hour-angle, and recalculate the latitude by a 
true method from both observations. If both latitudes are the same as from previous determina- 
tions it is a good guarantee of the correctness of position ; or 

With the resulting latitude recalculate the longitude from both observations. If they both 
agree with previous results we may rely with confidence on the correctness of the calculations, 
but of course this will not guarantee the correctness of position if a wrong altitude has been 
observed or a wrong declination used in the calculations. 



FOR DETERMINATION OF LATITUDES. 



A. 

A.T. Green. 
Long. 44 37-2' W 

A.T. Sp. 

H.A. East 
Alt. 

Azim. S. 42 53' E. 


M. Observation. 

H. M. S. 

2 54 54 
. 2 58 29 


P.M. Observation. 

H. M. S. 

A.T. Green. 3 i 30 
Long. 44 38-7' W. 2 58 35 


23 56 25 

o 3 35 

88 41' 

gives Redn. 


Sin. 
Sec. 

Sin. 


8-1941 
1-6387 


A.T. Sp. West o 2 55 
Alt. 88 47-4' 

Azim. S. 37 4' W. gives Redn. 
at i min. = 5-03' x 2-92 
min. = Red. 14-7'. 


Sin. 
Sec. 

Sin. 


8-1047 
8-6754 


.6-7801 


9-8328 





at i m. = 5-89' x 3-58 m. 
= Red. 21-1'. 



True alt. Q 
Redn. 

Mer. alt. 

M.Z.D. 
Decl. 

Latitude 



88 41-08. 

+ 2I-I 

89 2-1 

o 57'9 N. 
o 37-oN. 

o 20-9 N. 



True alt. O 
Redn. 

Mer. alt. 

M.Z.D. 
Decl. 

Latitude 



88 47-4 S. 
+ 14-7 

89 2-1 

o 57'9N. 
o 37-0 N. 

o 20-9 N. 



A 
L 
P 


88 41 
o 21 Sec. 
90 37 Cosec 


o-oooo 
o-oooo 




179 39 




S 
S - A 


89 49^ Cos. 
i 8* Sin. 


7-4849 
8-2994 


H.A. oh. 


3m. 34-55. Sin2 

A.T. Ship 
A.T. Green. 

Long, in time 

Longitude 
Run 


5-7843 


H. M. S. 
23 56 25-5 

26 54 54-0 


2 58 28-5 


44 37-i'W. 

1-5 w. 



DETERMINATION OF LONGITUDES. 



Longitude at time of 2nd obsn. 44 38-6' W. 



88 47 24 

O 21 O 

90 37 o 



~ A 



179 45 24 



9 52 42 
i 5 18 



H.A. oh. 2 m. 54'6s. 



Cos. 
Sin. 



A.T. Ship 
A.T. Green. 



H. M. s. 

O 2 54-6 

3 i 30-o 



Long, in time 2 58 35-4 
Longitude 44 38-8' W, 



7-3270 
8-2786 



5-6056 



NOTE. The determination of latitude by the use of Table VIII should only be made within 
the limits of time given in Tables VII or VIlA, as it will not give a true result outside these 
limits. 



162 

SUMNER" POSITION FROM A.M. AND P.M. SUN OBSERVATIONS NEAR THE 

MERIDIAN. 



1898. On August 3ist, in lat. by D.R. 7 42' N., long. 73 50' E. Obsd. alt. of 0's L.L. (a.m. 
at ship) was 88 50' N. when a chronometer indicated M.T.G. 30 d. 19 h. 2m. 535., and again (p.m.) 
the obsd. alt. of 0's L.L. was 88 44' when chronometer indicated M.T.G. 3od. igh. 7m. 575. 
Run in interval, N. 80 W., im., gives 0-2' N., i-o' W. Height of eye, 35ft. Required, posn. 
of ship by " Sumner's " method from ex-meridian tables. 



A.M. Observation. 



M.T. Green. 
Long. 73 50' E 

M.T. at ship 
Eq. time 

A.T. Sp. 
H A 


D. H. M. 
3 ig 2 

4 55 


s. 
53 

20 


Obsd. alt. Q's L.L. 
Cor. 35ft. (p. 87) 

True alt. -- 
Redn 

Mem Alt. 


88 50 N Ed 

+ 10 


Decl. 3 ist 
54'4" x 5h. 

Decl. 

Eq. of time 
785. x sh. 


8 33 oN 
+ 4 32 


23 58 


13 
13 


89 o'o 
+ 7-8 


8 37 32 N 


M. S. 

o 9-36 
+ 3'9 


23 58 





89 7-8N 


F. ? 




^^^^ 



Cor. Eq. T. o 13-26 



For Azimuth and Reduction. 



H.A. 
Decl. 
Alt. 

Az. 



2m. Sin. 7'94o8 
8 37^' Cos 9-9951 
3 9 Sec. 1-7581 



29 37i' Sin. 9-6Q40 



gives (p. 4o) A & B 178' gives (p. 75) 
position-line for plane chart N 60-7 W., 
and (p. i46) Redn at i min. 3-92' x 2 m. 
= Redn 7-8'. 



For the Latitude. 



89 7.8 N 

o 52-2 S 

8 37-5 N 



Mem Alt. 

M.Z.D. 
Decl. 

Lat. 
Run. 



Lat. at time of 2nd Obsn 7 45-5 N 



P.M. Observation. 



M.T. Green. 
Long. 73 49' E 

M.T. at Sp. 
Eq.T. 

A.T. Sp. 
H.A. 


3 J9 7 57 
+ 4 55 16 


31 o 3 12 

- 13 


31 o 3 o 


W. 3 o 



For Azimuth. 



H.A. 
Dl. 

Alt. 

Az. 



3m. 
8 374' 

88 54' 

42 24' 



Sin. 
Cos. 
Sec. 



8-1169 
9'995i 
17168 



Sin. 9-8288 



gives (p. 40) A & B i'ii' gives (p. 37) position-line for 
plane chart N 48 E, or S 48 W., and (p. 145) 
Redn at i min. 5-76' x 3m. = Reduction 17-3' 



For the Latitude. 



Obsd. alt. 0's L.L. 
.35ft. cor. 

T. alt. -O- 
Redn 

Mem Alt. 

M.Z.D. 
Decl. 

Latitude 



88 44N Wd 
+ 10 

8854N 
+ 17-3 

"89"^ N 



o 48-7 S 
8 37-5 N 

7 48-8 N 





73 


t5O Position worked withot 


it the Aid of Chart. 

29 J E. (Table M) 0^6 N. to W 
*2 W. 0-91 3. to W 




X 




7150'N Ist lat> 7 45 ' 5 N - O' s Az - N - 
and. lat. 7 48-8 N. N. 




d. lat. 3-3 


lat. error (Sum.) 1-47 to i-o long. 

long. cor. i a t. cor . 
2-25' x 0-56' = 1-26' N 

Long. (2) 73 49-0 E 
Cor. o 2-3 W 

Long, in 73 46-7 E 


lat. error long. d. lat. 
1-47' : i-o' :: 3 '3' 

4 *' Lat. (i) 7 4y5 N 
*f Cor.^ o 1-3 N 

Lat. in 7 46-8 N 



Position from chart : 
Latitude 7 46!' N., longitude 73 46^' E. 



NOTE. The long, by chron. at 2nd observation, calculated with this lat. found from the two 
observations, was 73 46' 30" E., and the lat. reworked from the H.A. resulting from this long was 
7 47' N. 



163 

POSITION BY CHRONOMETER AND EX-MERIDIAN OBSERVATIONS OF SUN AND 

MOON. 

1898. On March 3oth, at about i h. 24m. p.m., at ship, observed alt. of d 's U.L. was 27 57' 
east of meridian when a chronometer indicated M.T.G. 2h. i8m. 573., and after running on an east 
course 2 miles the G's L.L. was observed to be 32 51' when the chronometer indicated 2h. 26m. 
353. Lat. by D.R. 58 2^' N., long. 12 30' W., height of eye 35ft. 



M.T. Green 
Sid. T. (G. noon) 
Accl. 2h. 19 m. 

Sid. T. Green. 


D. H. M. S. 

30 2 18 57 
+ 31 34'8 
+ 22-8 

2 50 54'6 


1st Observation, d 

Obsd. alt. d's U.L. 2757 o 
Dip. 35ft. - 5 50 


A 
L 
P 

S 
S - A 

H. 

H.A. 4 
d's R.A. 6 


28 22* 

58 2! Sec. 
66 15 Cosec. 

152 40 


0-27630 
0-03843 

9'3734i 
9-87079 

9'55893 


27 5i 10 
Semi-d. - 14 58 


H. M. S. 

d's R.A. 2 hrs. 6 55 51-6 
2-133. x 19 m. + 40-5 


App. alt. d 's centre 27 36 12 
Cor. T. (39, Raper) ) fi 
H.P. 54' 16" 


76 20 COS. 

47 57i Sin. 

M. S. 

56 o Hav. 
56 32-1 


T. alt. d 's centre 28 22 27 


A -459 S. 
B -458 N. 

C -ooi S. ' 
gives Az. 90 


Cor. R.A. 

d 's decl. 2 hrs. 
5-44" x 19 m. 

Cor. decl. 
P.D. 


6 56 32-1 


Sid. T. Sp. 2 
Sid. T. G. 2 


o 32-1 
50 54'6 


23 46 57 N. 
- i 43 


Long, in time 


50 22-5 


Long. 12 
Run 


35 38 W. 

3 48 E. 


23 45 14 N. 


Long. at2ndobsn. 12 


31 50 W. 


66 14 46 N. 


Long, in time sc 


>m. 7-38. 



Run east 2m. = d. long. 3-8' E. 
2nd Observation, Q. 
LAT. BY EX-MERIDIAN TABLE No. 2. 

By reference to page 152 it will be seen that with, a low latitude and high declination this 
table may be used without appreciable error to about 2 hours from the meridian. Therefore, by 
transposing lat. and dec.' the same wide range may be obtained. The example below illustrates 
this case. 



H. M. S. 

M.T.G. 2 26 35 
Long. W - 50 7'3 



Obsd.alt.of O'sL.L. 32 51 S. 



35 ft. cor. (p. 87) 



+ 9 



O's decl. 3 53 21 N. 

58-2" x 2-4 hrs. 2 20 N. 



M.T. Sp. i 36 27-7 
Eq. T. - 4 27-0 



H.A. 



i 32 0-7 



Lat. (dec.) 3 56 N ) A -16 S. 
Dec. (lat.) 58 o N j B 4-10 N, 



T. alt. 
Redn. 

Mer. alt. 

M.Z.D. 
Decl. 


33 o-o S. 

2 55'2 


Cor. decl. 

Eq. time 
?6s x 2-4 hrs. 


3 55 4i N. 


M. S. 

4 28-8 
- 1-8 


35 55'2 


54 4'8 N. 
3 55'7 N. 



1-904' x 92m. 



C 3-94 N. gives (p. 153) 
I75'i68' = 2 55-2' redn. 



Lat. 



58 0-5 N. 



Cor. Eq. T. 



4 27-0 



CORRECTNESS OF WORK BY THE ABOVE METHODS WITH EX-MERIDIAN TABLE No. 2 

PROVED BY RIGOROUS CALCULATION. 



H.A. 
Decl. 


H. M. 
I 32 

3 55' 41" N 


Cos. 9-964026 
Cot. i '163267 


Cosec. 1*164289 


Arc (i) 


4 15 58 N 


Cot. 1-127293 


Sin. 8-871502 






O's alt. 33 o' 


Sin. 9-736109 


w (2) 

















Lat. 



58 o 28 N. 



As the moon was on the prime vertical when the altitude was taken, the time deduced from this 
-observation should be absolutely correct, and the latitude by ex-meridian of the sun will also be 
correct without any additional work. 

See note on page 117 about correcting moon's semidiameter and horizontal parallax for 
.Greenwich date. 



164 



POSITION OF SHIP FROM COMBINED EX-MERIDIAN OBSERVATIONS OF TWO 
STARS, USING STAR-REDUCTION AND AZIMUTH EX-MERIDIAN TABLES. 



1917. -On March 26th, soon after sunset, at about 6h. 5m. and 6h. 12 m. p.m., in 
approximate latitude 18 S., and longitude D.R. 3 36' W., the true altitude of * Capella was 
24 5' N.Wd., when chronometer showed M.T.G. 6 h. 24 m. 18 s., and after running N. 45 W. 
1 1 miles the true altitude of * Sirius was 87 io|' N.Ed, when chronometer showed 6 h. 31 m. 
175. Required, the position of ship at 2nd observation. Run N. 45 W. 1-5 m. = i-o' N. 
i-i' W. 



H. M. S. 

M.T. Green. 6 24 18 

Long. 3 36' W. o 14 24 



# CAPELLA TO NORTH-WESTWARD. 

24 5-oN. 



* SIRIUS TO NORTH-EASTWARD. 



#'s Alt. 
Redn. 



M.T. Ship 
Sid. T.G. noon 
Accl. 

Sid. T. Ship 
*'s R.A. 

*'s H.A. W. 



6 9 54 
o 13 26 



6 24 23 
5 10 35 

i 13 48 



Mer. alt. 



M.Z.D. 
Decl. 



26 14-1 



63 45-9S. 

45 55'i N 



Gives (p. 319*) Redn. 2 9-1' 
and Azim. N. 14 W. 



Lat. 17 50-8 S. 

Run i-oN. 

Lat. at time I 17 49-88. 
of 2nd obsn. ) ^^^. 



For Position-line on Plane Chart. 

Az. N. 14 W. gives (Table IV, p. 260*) lat. var. 17-0 s.j 
which gives (p. 270*) posn.-line S. 76-8 W. 



Position on chart 
True position 



17 51-4 S. and 3 43-5 W, 
17 5i'i S. 3 43-3 W. 



H. M. S. 

M.T.G. 6 31 17 

Long. 3 37' W. 14 28 



M.T. Sp. 
S.T.G.N. 
Accl. 



6 16 49 
o 13 26 
+ i 4 

6 31 19 
6 41 31 



S.T. Sp. 
*'s R.A. 

*'s H.A. E. 



Decl. 16 36'-3S. 

Alt. 87 10-5 N. 



Azim. N. 59 54' E. gives 



#'s Alt. 
Redn. 



Mer. alt. 



M.Z.D. 
Decl. 



Latitude 
Sin. 8-6483 



87 10-5 N. 
+ 1 23-8 



i 25-78. 
16 36-38. 

18 2-0 S. 



Cos. 

Sec. 



9-9815 
1-3073 



Sin. 9-9371 



(p. 291*) Redn. at i min. 8-22' x 10-2 m. = Redn. 83- 



For Position-line on Plane Chart. 
Az. N. 59-9 E. gives (p. 258*) lat. var. 2-44 s., 
which gives (p. 270*) posn.-line N. 31-4 W 



56' 



Pos" 




-221 



* Page references to "Tables of Calculated Hour-angles," &c., by Blackburne. 2nd Edition. 



165 



Extract of Azimuth Ex=meridian Table, from Blackburne's New Book. 



^0 


AZIMUTHS. 


3 










2 


o 


o 


o 











c 


c ! o 





O O 


O 


3 


58-6 


58-7 


58-8 


58-9 


59-0 


59-1 


59-2 


59-3 


59-4 


59-5 


59-6 


59-7 


59-8 


59-9 


60-0 




REDUCTION TO THE MERIDIAN AT HOUR-ANGLE OF i MIN. 






















/ 1 / 


o 


8-42 8-43 


8-45 


8-47 


8-49 


8-50 8-52 


8-54 8-56 


8-57 


8-59 8-61 


8-63 


8-64 j 8-66 


-2. 


8-41 8-43 


8-45 


8-46 


8-48 


8-50 i 8-52 


8-53 8-55 8-57 


8-58 


8-60 8-62 


8-64 


8-65 


4 


8-40 


8-41 


8-43 


8-45 


8'47 


8-48 : 8-50 


8-52 8-54 8-55 


8-57 


8-59 


8-61 


8-62 


8-64 


6 


8*37 


8-39 


8-41 


8-42 


8-44 


8-46 


8-47 


8-49 


8-51 


8-53 


8-54 


8-56 


8-58 


8-60 


8-61 


8 


8-34 


8-35 


8-37 


8-39 


8-40 


8-42 


8-44 


8-46 


8-47 


8-49 


8-51 


8-52 


8-54 


8-56 


8-58 


9 


8-31 


8-33 


8-35 


8-37 


8-38 


8-40 


8-42 


8-43 


8-45 


8-47 


8-48 


8-50 


8-52 


8-54 


8-55 


10 


8-2g 


8-31 


8-32 


8-34 


8-36 


8-37 


8-39 


8-41 


8-43 


8-44 


8-46 


8-48 


8-49 


8-51 


8-53 


II 


8-26 8-28 


8-30 


8-31 


8-33 


8-35 


8-37 


8-38 


8-40 


8-42 


8-43 


8-45 


8-47 


8-48 


8-50 


12 


8-23 \ 8-25 


8-27 


8-28 


8-30 


8-32 


8-34 


8-35 


8-37 


8-39 


8-40 


8-42 


8-44 


8-45 


8-47 


13 


8-20 8-22 


8-23 


8-25 


8-27 


8-29 


8-30 


8-32 


8-34 


8-35 


8-37 


8-39 


8-40 


8-42 


8-44 


I4 


8-17 8-18 


8-20 


8-22 


8-23 


8-25 


8-27 


8-29 8-30 


8-32 


8-34 


8-35 


8-37 


8-39 


8-40 


15 


8-13 8-15 


8-16 


8-18 


8-20 


8-21 


8-23 


8-25 8-26 8-28 


8-30 


8-31 


8-33 


8-35 


8-36 


16 


8-09 8-n 


8-12 


8-14 


8-16 


8-17 


8-19 


8-21 8-22 


8-24 


8-26 


8-27 8-29 


8-31 


8-32 


T 7 


8-05 


8-07 


8-08 


8-10 


8-12 


8-13 8-15 


8-17 8-18 8-20 


8-22 


8-23 8-25 


8-27 


8-28 


18 


8-01 


8-02 


8-04 


8-05 


8-07 


8-09 8-10 


8-12 


8-14 8-15 


8-I 7 


8-19 


8-20 


8-22 


8-24 



EXAMPLE FROM PREVIOUS PAGE WORKED FROM TWO CALCULATED 
LONGITUDES AND PLOTTED ON PLANE CHART. 



s. 

S- A 



K CAPELLA TO N.Wo. 

H. M. s. , 

M.T.G. 6 24 18 True Alt. 24 5 

M. Q's R.A. o 14 29 

Sid. T.G. 6 38 47 



M.T.G. 6 31 17 

M. Q's R.A. o 14 30 



Sid. T.G. 



SIKIUS ro N.ED. 
s- 

True alt. 



87 



6 45 47 



Run N. 45 W. 1-5 m. = i'o' N. i'i' W. 



24 5 o 

17 49 o 

135 55 6 

177 49 6 



Sec. 0-0213 
Cosec. 0-1576 



-96 N. 



87 10 30 
17 48 o 
73 23 42 



Sec. 0-0213 
Cosec. 0-0185 



Cos. 
Sin. 



88 54 33 
64 49 33 



*'s H.A. West 
*'s R.A. 

Sid. T. Ship 
Sid. T. Green. 

Long, in time 



Longitude 
Run 

Long at time of 2nd 
obsn. 



8-2796 
9-9567 



C. 



Sin.2 8-4152 



178 22 12 

S. 89 ii 6 

Gives posn.-line S A 2 o 36 
S. 76-6 W. 



Cos. 
Sin. 



8-1530 
8-5450 



Sin.2 6-7378 



A. 6-86 N. 

B. 6-388. 

C. 0-48 N. 

Gives posn-linfr 
S. 25* E. 



H. M. S. 
I 14 15 

5 10 35 

6 24 50 
6 38_47 

o 13 57 



3 29 15 W. 
i 6 W. 

3 30 21 W. 



#'s H.A. East 
#'s R.A. 

Sid. T. Ship 
Sid. T. Green. 

Long, in time 
Longitude 


H. M. S. 

-o 10 43 
6 41 31 


6 30 48 
6 45 47 

o 14 59 


3 44' 45" W. 



Position on chart 17 51-18. and 3 43-3 W. 



NOTE. To get accurate results with so high an altitude when working from the meridian 
the D.R. longitude should not be more than 5' or 6' in error if the azimuth is large, or when 
working from a parallel of latitude the D.R. latitude should not be much in error when the 
azimuth is small. The slight error (o') in latitude from the ex-meridian observation is due to 
neglect to interpolate in the reduction table for * Capella for .10' of error in the D.R. latitude, 
and the 0-3' of error in the longitude is due to curvature in the position-line in 12 J' of arc, with 
a small Z D. 



166 



POSITION OF SHIP BY COMBINED OBSERVATIONS OF SUN AND PLANET VENUS. 
LONGITUDE AND EX-MERIDIAN OBSERVATIONS. 

1917. December 2gth, p.m. at ship, in approximate latitude 30 S., the true altitude of 
sun's centre was 52 3' when a chronometer (corrected) indicated M.T.G. i h. 51 m. 58 s., and 
about the same time the true altitude of planet Venus (centre) was 74 43' N. when chronometer 
(corrected) indicated M.T.G. i h. 53 m. 15 s. Run in interval N. 41 W. 0-3 m. = d. long.o' i5"W. 
Required, position of ship at time of second observation. 



Q P.M. Observation for Longitude. 



H. M. s. 

M.T. Green. i 51 58 
Eq. time 22 



A.T. Green. i 49 56 



True alt. -6- 52 3 W. 
Decl. 23 158. 



Lat. 30 oS. ) 
Decl. 23 X5S.& 

Alt. 52 3 ) 



By Blackburne's Hour-angle Tables. 

s. , s. 

Dl. var. + 1-56 x 15 = -f 23-40 
Alt. var. 4-62 x 3 = 13-86 



Cor. to Tabular H.A. 
Gives H.A. 



30 S. 

238. 
52 



Cor. A.T. Ship 
A.T. Green. 

Long, in time 

Longitude 
Run 



+ 9'54 

H. M. 

2 47 54-2 

2 48 3-7 
i 49 56-0 

o 58 7-7 

14 31 55 E. 
15 W. 



Long, at time of 2nd obsn. 14 31 40 E. 



Planet Venus. Ex-meridian for Latitude. 



M.T. Green. 
Sid. T.G. noon 
Accl. 

Sid. T. Green. 
Long. E. 

Sid. T. Sp. 
#'s R.A. 


H. M. S. 

i 53 15 
18 29 28-7 
+ 18-6 


True alt. of 
Reduction 

Mer. alt. 

M.Z.D. 
Decl. 

Lat. 


* 74 43-o N. 
+ n-5 


74 54'5 

15 5-5S. 
15 4-8 S. 


20 23 2-3 
o 58 6-7 




21 31 39 


30 10-38. 



H.A. 10 30 E. 



For Azim. and Reduction. 



H.A. 

Dl. 

Alt. 



M. S. 

10 30 Sin. 8-6609 

15 5 Cos. 9-9848 

74 43 Sec. 0-5791 



E. gives 
cor. 6-80' 



Az. N. 9 
A. and 
which gives Redn. at 
i min. = i-io' x 
10-5 m = Reduction 
n-55'. 



Sin. 9-2248 



H.A. 
Dl. 
Arc. (i) 



Latitude by Spherical Calculation. 
M. s. 
10 30 Cos. 9-999544 

15 4 4*8 Cot. 0-569527 

15 5 42|S. Cot. 
Alt. 



0-569071 



74 43 



Cosec. 0-584747 
Sin. 9-415679 
Sin. 9-984363 



(2) 15 4 33 S Cos. 9-984789 

Lat. 30 10 



True Position. 

Lat. 3o 10-38. 

Long. 14 31-7 E. 



NOTE. As the sun was on the prime vertical when the observation for longitude was taken 
10' of error in the latitude worked with makes no difference in the longitude; the hour-angle 
deduced from this longitude for calculation of ex-meridian would be correct, and consequently 
the latitude by ex-meridian will also be correct without any plotting on the chart or further 
calculation. The hour-angle worked by direct spherics by logarithms gives exactly the same 
result to the decimal of a second. 



167 



POSITION FROM TWO STELLAR OBSERVATIONS. 

(COMBINING CHRON. LONG. OBSERVATION WITH AN EX-MERIDIAN BELOW THE POLE.) 

1898. On October 8th, at about 6h. 44111. p.m. A.T. at ship, observed altitude of * Canopus 
east of meridian was 15 14' S., when a chronometer indicated mean time at Greenwich yd. igh. 
36m. i6s., and after running on a true S. 55 E. course for three-quarters of a mile observed 
altitude of * Fomalhaut to north-eastward was 49 20', when chronometer indicated yd. 19 h. 
40 m. 6s. Height of eye, 28 ft. Required, true bearing of stars and position of ship at time of 
second observation, the approximate position at the time being latitude 51 S. and longitude 163 E. 



M.T.G. 

Long. 162 59' E. 

M.T. Sp. 
M. Q's R.A. 

Sid. T. at Sp. 
*'sR.A. 



H.A. 
Supt. 



D. H. M. S. 

7 19 36 20 
+ 10 51 56 

8 6 28 16 
+ 13 7 50-2 

19 36 6'2 
- 6 21 43 

13 14 23'2 W. 



i 14 23'2 E. 
H.A. at Inferior Transit. 



Az. from Table* 


S. nj E. 


Position-line 


N.78J E. 


M.T.G. 
Sid. Time 
Accl. 


D. H. M. S. 

7 19 40 6 
+ *3 4 37 



# CANOPUS TO SOUTH-EASTWARD. 

o t 

Obsd. alt. * Canopus 15 14*0 S. 
Cor. 28ft. - 8-7 



True alt. 

Red". from Table* 



Mer. alt. 
P. Dist. 



Lat. 
Run 



Lat. at 2nd obsn. 



15 



Sid. T. (G. noon) 
Accl. igh. 36^m. 

.A. 



13 54-5 S. 
37 22-0 S. 

51 16-5 S. 
0-4 S. 



tt'sDecl. 
P. Dist. 



H. M. S. 

13 4 37'0 

+ .3 i3'2 
13 7 50-2 



52 38 S 



37 22 S. 



51 16-9 S. 



Run S. 55 E., 075 m. = 0-4' S., 0-6' E. 
= i-o' E. 



Sid. T.G. 



8 47 56-9 



FOMALHAUT TO NORTH-EASTWARD. 

Obsd. alt .of # Fomalhaut 49 20-0 
Cor. 28ft. - 6-0 

True alt. 49 14-0 



K'sDecl. 
P. Dist. 



30 9 24 S. 
59 50 36 



S 

S- A 



49 *4 
51 o 
59 5i 

160 5 

80 i\ 
30 48^ 



Sec 

Cosec 0-06313 



Cos 
Sin 



9-23787 
970941 



Sin? 9-21154 



*'sH.A. 
*'sR.A. 

Sid. T. at Ship 
Sid. T. at Green 

Long in Time 
Longitude 


H. M. S. 

3 10 20-6 E. 
22 52 57 


8 47 57 


10 53 48 


163 27' o" E. 



1-13 N. 
079 S. 

0-34 N. gives Azimuth N. 78 E. 

Position-line S. 12 E. 




Position of ship, 51 i2|' S. 163 31^' E. 

NOTE. As time is often lost in getting hold of the log-book and working up the D.R. position, 
this example is worked with the nearest whole degree of latitude and longitude, and this will generally 
be near enough for a pretty accurate result when working by the improved " Sumner " method. 
This problem worked closely by spherics gives within ' of same result.. 



* Blackburne's and Westland's " Reduction and Azimuth Tables.' 



168 

TO FIND APPROXIMATE ALTITUDES AND BEARINGS OF SUITABLE STARS FOR 
OBSERVATION TO QUICKLY OBTAIN POSITION OF SHIP.* 

1917. On July 9th, soon after sunset, at about 7 h. 50 m. p.m. and 7 h. 54 m., in approxi- 
mate latitude 47 N. and longitude 7 W., find what stars of first magnitude within the limits 
of the Reduction and Azimuth Tables would be suitable for quickly determining the ship's 
position, and the approximate altitudes and bearings of the stars. Height of eye, 40 ft. 

First find the Sid. Time at ship= A.T. Sp. + A. Q's R.A. 

H. M. 

A.T. Sp. 7 50 Next look up Table of Stars in order of R.A. (p. 283) and see what stars in adjacent quad- 

A. O's R.A. +713 rants come within the limits of this Sid. Time. 

It will be seen at a glance that Capella to N.W. and Arcturus to S.W. are the two most 
Sid. T. Sp. 153 suitable stars. 



Sid. Time 
# Capella 

Mer. Pass. 
K's H.A. 
Lat. 
Gives Redn. 



H. M. 
15 3 

17 ii below 
Pole. 

2 8) 

4 4 " 



and Azim. N. 22 W. 



*'s Decl. 

P.D. 
Lat. 

Mer. Alt. 
Redn. 
Cor. 40 ft. 



45 54-9 N. 

TTTiN. 

47 o-oN. 



+ 4 8-8 
+ 13-7 



Sid. Time 
# Arcturus 

Mer. Pass. 
*'s H.A. 
Lat. 



H. M. 

15 7 

14 12 



o 55) 
47 N.f 
Gives Redn. 2 13' 
and Azim. S. 27 W. 



Alt. for sextant 7 17-4 N. 



#'s Decl. 
Lat. 



M.Z.D. 



Mer. Alt. 
Redn. 



True Alt. 
40 ft. Cor. 



19 36-7N. 
47 o-oN. 

27 23-3 
62 36-78. 

-2 13 



60 23-7 

+ 7 



Alt. for sextant 60 30-78. 



POSITION FROM COMBINED ALTITUDES OF TWO EX-MERIDIAN STARS. 

1917. On July gth, soon after sunset, at about 7h. 50 m. p.m., in approximate latitude 
47 N. and longitude 7 W., the true altitude of # Capella was 7 2-2' N.W., when chronometer 
showed M.T.G. 8 h. 23 m. 48 s., and true altitude of # Arcturus was 60 23-7' S.W-, when chro- 
nometer showed M.T.G. 8 h. 26 m. 59 s. Run in interval N. 32 E. 0-7 m. Required, position 
of ship at time of 2nd observation. 

# CAPELLA TO N.W. 



M.T.G. 
Long. 7 W. 

M.T. Sp. 
M. O's R.A. 

Sid. T. Sp. 
*'s R.A. 

*'sH.A. 
Supt. or below Pole 


H. M. S. 

8 23 48 
28 o 

7 55 48 
+ 7 8 47 


Alt. of * 
Redn. 

Mer. Alt. 
*'s P.D. 

Approx. Lat. 
Cor. for 6' 

Lat. 
Run 

Lat. at time of 


7 2-2 N. 
4 i'3 


Sid. T.G. Noon 
Accl. 8 h. 23* m. 

M. O's R.A. (i) 
Accl. 3 m. 

M. O's R.A. (2) 
*'s Decl. 4 5 54 


H. M. S. 

7 7 24-7 

+ 1 22-7 


3 0-9 

44 5-i N. 

47 6-oN. 
+ 0-4 


7 8 47-4 
+ 0-5 


15 4 35 
-5 10 35 


7 8 47-9 


-9 54 oW. 

1200 


47 6-4 N. 
0-6 N. 


2 6 oW. 


2nd 47 7-oN. . 


P.D. 44 5 


iN. 



Gives from Reduction and Azim. Table (p. 346) 

Redn. 4 1-3', Azim. N. 21^ W. ; Posn.-line S. 68A W. 



Run N. 32 E. 0-7 m. = 0-6' N. 
0-4' E. d. long. 0-5' E. 



H. M. s. 

M.T.G. 8 26 59 

Long. 6 59^' 27 58 



M.T. Sp. 7 5< 

M. G's R.A. +7 j 



Sid. T. Sp. 
*'s R.A. 



15 7 49 
14 ii 55 



*'sH.A. 



o 55 54 W. 



jives from Reduction and Azimuth 
Table (p. 325) Redn. 2 16-8' 
and Azim. S. 27^ W. ; Posn.- 
line N. 62^ W. 



ARCTURUS TO S.W. 

Lat(if 




ist Obs. Lat. 47 7-0 N. 
2nd ,, ,, 46 55'7N. 



Azim. N. 21'sW. gives 
S. 27-5 W. 



(Table IX, p. 301.) 

0-27 S. to W. 
0-35 N. to W. 



Lat. 
Cor. 



II 



Alt. of 
Redn. 



Mer. Alt. 



M.Z.D. 

*'s Decl. 



60 23-78. 
+ 2 16-8 

62 40-5 

27 I9-5N. 
19 36-7 



Approx. Lat. 46 56-2 
Cor. for 4' -5 



Lat. 



46 55-7 N. 



Long. (2) 6 59-5 W. 
Cor. i8-2W. 



Diff. Lat. 



11-3 



Lat. Error 0-62 to i' of long. Lat. 47 2 N. Ling. 



7 17-7 W. 



Lat. Error. D. Lat. 
0-62' : 11-3 



Long, 
i-o' 



Long. Cor. Lat. Cor. 

18-2' W. x 0-27' = 5-01' S. 



* This example is taken from " Tables of Calculated Hour-angles and Altitude Azimuths, Ex-meridian Tables, and 
Calculated Reductions and Azimuths of Bright Stars," by H. S. Blackburne. James Brown and Son, Glasgow. IDS. 6d. 



169 



POSITION FROM CALCULATED EX-MERIDIAN OF TWO STARS, EACH 
OVER FOUR HOURS FROM THE MERIDIAN OF INFERIOR 
TRANSIT. 

1898. On loth Nov., at about 7h. 25111. p.m. A.T. at ship in lat. by D.R. 40 
30' S. and long. 173 o' E. Observed altitude of * Canopus was 17 10' to S.E. 
when a chronometer indicated M.T.G. 9 d. 19 h. 35 m. 28 s., and again after running 
east (true) for |m. observed altitude of * a 2 Centauri 22 51^' to S.W. when a 
chronometer indicated M.T.G. 19 h. 37m. 483. Height of eye, 36ft. Required the 
position of ship at the time of second observation. 



D. H. M. S. 



IST OBSERVATION. 

H. M. s. 



CANOPUS TO S.Eo. 



M.T.G. 9 19 35 28 Sid. T. at G. noon 15 14 43-2 Obsd. alt. of # 17 10 
Long. i73 J E + 1132 o Accl. igh 354 + 313-1 36 ft. cor. - 9 


M.T. at Sp. 
M. O's R.A. 


7 7 28 M. O's R.A. (ist obsn.) 151756-3 T. alt. of X 17 i 
15 17 56'3 + "2 ' = 


Sid. T. at Sp. 
*'sR.A. 

*'sH.A. 
Supt. 

H.A. 
Decl 

Arc (i) 

. (2) 

Lat. 

M.T.G. 
Long. 173 

M.T.atSp 
M. O'sR-^ 

Sid. T. at S 
*'s R.A. 

*'s H.A. 
Supt. 

H.A. 
Dl. 

Arc (i) 
(2) 
Lat. 

La 
/ lony. ccr~. 


22 25 24-3 M. O's R.A. (2nd obsn.) 15 17 56-5 


6 21 44-3 A 0-473 S 
B 1-50 S 
7 56 20-0 E 


4 3 40 E , 
LATITUDE BY EX-MERIDIAN. dep. 1-500 gives Az. S 33 41 E 

H. M. S. ^ 

4 3 40 Cos 9-68671 Pos.-line S 56 19 W 
52 38' Cot 9-88289 , =; 
, Az. 33 41 Cos 9-92018 
20 21-9 S Tan 9-56960 Alt. 17 i Cot 0-51421 






40 33'5 S and posn.-line S 50-3 W .^ 


2ND OBSERVATION. 

H. M. s. FOR AZIMUTH. * a 2 CENTAURI TO S. Wn 
19 37 49 H. M. s. , 
o^' E ii 32 2 4 4 56 Sin 9-9428 Obsd. alt. of X 22 51-2 




i. 15 17 56-5 T. alt. of # 22 43-0 
Az S 27 59' W Sin 9*6713 


>p. 22 27 47-5 or posn.-line 
14 32 43'0 N 62 W 


7 55 4'5 W 


4 4 55'5 W 
LATITUDE BY EX-MERIDIAN. 

H. M. S. o / 

4 4 56 Cos 9-68236 Az. 27 59 Cos 9-94600 
fo 25' Cot 975411 Alt. 22 43 Cot 0-37815 


15 16-8 S Tan 9-43647 Arc (2) 25 21-9 Cot 0-32415 


25 21-9 S 


40 38-7 S and posn.-line N 62 W 


t. 40'33 ^'S Table M (page 156). 

ist obsn. Az. S. 34 E. and Lat. 40 33-5 S. gives -51 lat. error S. to Wd. 
2nd obsn. Az. S. 28 W. and Lat. 40 38-7 S. gives '41 lat. error N. to Wd. 


D. lat, 5-2 -^ -92 long. cor. 5-6' W. x '51' 


- = lat. cor. 2-86' S. 

23' Lat. (i) = 4033-58 Long, (i) 173 0-5 E 
Cor. 2-9 S Cor. 5'6 W 


La. 

NOTE. These 
had the second ex 


Lat. in 40 36-4 S Long, in 172 54*9 E 


observations worked as two chronometer problems gave exactly the same results, but 
-meridian latitude been worked with the azimuth as found by the A and B Tables the 



latitude would have been nearly i' in error, due to a slight change in the star's declination in twelve years ; 
the B Table having been calculated for X 's declination in 1910 It is well to remember, however, that 
the best results will always be obtained by using the sine method with hour-angle and altitude in the 
calculation of the azimuth, and this is especially the case where the altitude is high. 



170 

BELOW POLE EX-MERIDIAN AND POSITION-LINE. 

1910. On April ist, soon after sunset, at 6h. 42111. p.m., observed altitude of * a Cygni 
(Deneb) 8 46' W. of meridian when a chronometer indicated mean time at Greenwich 7 h. 34m. 135. 
Approximate latitude 52 'N., and longitude 12 W. Required, latitude of meridian, and position- 
line from it. 



M.T. Green. 
Long. 12 W. 

M.T. Sp. 
M. Q's R.A. 

Sid. T. at Sp. 
#'s R.A. 

*'sH.A. . 
Supt. 



646 
+ o 37 



7 23 19 

20 38 21 



10 44 58 W. 



H.A. at Inferior Transit. 



a CYGNI TO NORTHWARD. 
H. M. s. 



Sid. T. (G. noon) 
Accl. 7h. 34m. 



o 35 si'6 
+ i 14-6 

o 37 6-2 



Azimuth from table* N. 13-3 W. 

QO'O 



i 15 2 W. Position-line 



Obsd. alt. of # 
Cor. (40 ft.) 

T. alt. 
Redn. * 

Mer. alt. 
P.D. 

Lat. 

Cor. for 16' 

Lat. 



8 46-0 N. 
- 12-3 

8 337 

I 20'2 



7 13-5 N. 
45 2-9 N. 



52 16-4 N. 
+ 0-4 

52 i6'8N. 



-. 




The above example is given to draw special attention to the great value of the ex-meridian 
problem when near the meridian below the Pole. The observation gives with a minimum amount 
of work (when within the limits of these tables) the latitude on a certain meridian, and the position- 
line from this meridian. The curvature of this position-line is seen at a glance from the azimuth 
table, which is given on the same page as the reduction table. In this example the change of 
azimuth only amounts to 07 of a degree in 4m. of time, or i of longitude. 

The position-line at Loop Head would be N. 78 E. 

This position-line crossed by a bearing of Tearaght Island light (if sighted) would give a good 
reliable position, provided the observation was good. A sounding in conjunction with this position- 
line would also give a fairly accurate position. 

The latitude and position-line could also have been found at the same time from these tables 
by * Sirius, the position-line of which would have then been S. 79 E. The crossing of these two 
position-lines would give an excellent latitude, but the longitude would not be reliable, as the 
angle is small, and both observations are west of the meridian. 



From Blackburne's and Westland's "Azimuth and Reduction Tables." 1 



171 



FORMULA FOR CALCULATION OF EX-MERIDIAN LATITUDE WHEN 
AZIMUTH IS KNOWN. 

It will be seen from the accompanying figure that if we drop a perpendicular on 
the meridian from D at M the following arcs, P M arc (i), and Z M arc (2), are 
readily calculated. The sum or difference of arc (i) and arc (2) = latitude. 

Rule for Object above the Pole. 

Name arc (i) same as declina- 
tion. 

Name arc (2) contrary to bearing 
of object i.e., N. or S. of 
the prime vertical. 

Add like and subtract unlike 
names, which will give the 
required latitude. 

Formula of Calculation. 

Cot. PM arc (i) = Cos H.A. 

X Cot. decl. 
Tan Z M arc (2) = Cos. Az. 

X Cot. Alt. W 

Rule for Object below the 
Pole. 

Name both arc (i) and arc (2) 

same as the decl. 
Latitude = Sum of arc (i) 

and arc (2). 

For mules for the Calculation. 

H.A. = Supplement ot H.A. 

from upper meridian. 
For Arc (2) use comp. of Z M, 

or M N, then 
Tan. arc (i) = Cos. H.A. x 

Cot. decl. 
Cot. arc (2) = Cos. Az. x Cot. 

alt. 
P M + M N = comp. P Z = 

latitude. 

Arc (i) is found by the same formula as is used on p. 97, and the same arc 
is used for arc (2), but with a trifle less work; and as an ex-meridian outside the 
ordinary limits of ex-meridian tables is seldom of much use without the azimuth, 
this method is recommended in preference, if the azimuth is calculated with the 
H.A. and altitude. This method should always be used in preference when the 
declination of object is small. The writer's attention was first drawn to this excellent 
method of obtaining the latitude by a letter to the Nautical Magazine, August, 
1899, p. 581, from E. S. Haynes, master of the tug " Cuzuni," and the value of it 
has been further impressed on him by a study of Admiral H. E. Purey Gust's 
valuable little book on " Sumner's " method. In this work Admiral Cust, R.N. 
(late Hydrographer to the Admiralty), strongly advocates this method. 

Formula to compute Altitudes. 

Using the accompanying figure. From Z drop a per p. on the hour circle at N. 
This will be outside the usual spherical triangle when the hour-angle is over 6h. 
Arc (i) = PN. Arc (2)=PD-PN = ND when H.A. is less than 6h. Arc 
(2) = P D + P N when H.A. is more than 6h. Then Tan. Arc (i) = Cos. P X Cot. 
Lat. 

Sin. Alt. = sin. lat. x sec. arc (i) X Cos. arc (2). 
H.A. 6 h . = 90 Formula. 

Sin. Alt. = sin. decl. x sin. lat. 

12 A/imuth. 




30 N. 



FIGURE SHOWING : 

Latitude, 60 N. Declination, 
Hour-angle, 2 hours. 

Arc (i), PM or comp. QM. 

Arc (2), Z M or comp. M N or MS. 



173 



ILLUSTRATING THE 



RULE OF THE ROAD FOR SAILING-SHIPS, 

BY 

H. S. B l_ A O K B U R N E, 

WITH WHICH ARE EMBODIED THE 

" REGULATIONS FOR PREVENTING COLLISIONS AT SEA." 

PUBLISHED BY J. D. POTTER, 145 MINORIES, LONDON E., AND BY H. S. BLACKBURNE, WELLINGTON 

NEW ZEALAND. 

PRICE, 2s. NEW ZEALAND, 2s. 3D. 



EXTRACTS FROM LETTERS TO THE AUTHOR BY NAUTICAL EXPERTS. 



From CAPTAIN E. W. OWENS, Examiner, Local Marine Board, London. 

" I certainly have no objection to make, but much approval ; your work is concise, clear, and, from 
my point of view, correct." 

From CAPTAIN R. W. ESPINASSE Examiner to the Marine Board of Victoria, Australia. 

Letter to Editor of " Nautical Magazine," published March, 1904. 

" Captain Blackburne is well known for diagrams with explanations ' Illustrating the Rule of the 
Road for Sailing-ships.' . . . This booklet Is worthy of praise as the clearest and most original view 
of the subject yet made public." 

NAUTICAL ASSESSORS AND TEACHERS OF NAVIGATION. 

CAPTAIN A. WOOD, N.A. and Teacher of Navigation. 

" I think they will be very useful to candidates getting up the Rule of the Road. I especially like 
your treatment of two vessels close-hauled on the same tack, Diagram I." 

CAPTAIN SAML. BROOKS, N.A. 

" Your diagrams are excellent, and I think every officer in charge of a watch on board ship should 
have a copy of your book for his own information." 

CAPTAIN J. T. CASTLE, N.A. 

" It is well thought out, and you are to be congratulated on the simple and efficient manner in 
which its problems are presented. You may rest assured that its production will be of great service to 
those who wish to study so important a subject as that of knowing what means to adopt in order to 
3 void a collision when meeting or crossing another sailing-vessel." 

CAPTAIN G. KENNETH-HORE, N.A. 

" It seems to me that you have taken great pains to make a clear explanation of the ' weather rule ' 
position, and, what is sometimes a very difficult question to determine, how a vessel is steering when 
her green light is seen three points on the port bow of your own vessel, which at the same time has the 
wind on her port beam, and what is to be done under these circumstances." 

CAPTAIN J. NETHERCLIFT JUTSUM, Principal of the Nautical Academy. 

61 FITZHAMON EMBANKMENT, CARDIFF. 

" Many thanks for your little book re Rule of the Road. I consider it is as near perfection as any 
graphic method could be brought for illustrating this subject, and, although it is striking in its sim- 
plicity, its conciseness bears the impress of very careful and painstaking consideration in its production." 

CAPTAIN GEO. SHIELDS, Principal of Naval Academy, 40 CLYDE PLACE. 
" Allow me to thank you for the copy of your book, which is perfection itself. I wish you every 
success, and shall be pleased to recommend it to my pupils at all times." 

CAPTAIN JOHN OWEN, Principal of the Nautical School, 48 LONDON SQUARE, CARDIFF. 
" I thank you for your diagrams of the Rule of the Road for Sailing-ships. I think the illustrations 
are very good, and better than anything I have seen before on this most important subject." 



REVIEWS FROM THE PRESS. 



SHIPPING GAZETTE. 

" There is good reason to anticipate that appreciation of these diagrams will not be limited to can- 
didates for Board of Trade certificates, and we have no doubt that many officers at sea will find them 
of valuable and very practical assistance." 

THE SHIELDS DAILY GAZETTE AND SHIPPING TELEGRAPH. 

" Captain Blackburne, a well-known name in nautical circles, has just rendered a signal service to 
his seafaring confreres. His diagrams, with explanations, illustrating the new Rule of the Road, are 
marked with simplicity and distinctness. His little and unpretentious work ought to be in the hands 
of every master of a sailing-ship." 



174 

TABLES FOR AZIMUTHS, GREAT-CIRCLE SAILING, 

AND 

REDUCTION TO THE MERIDIAN, WITH A NEW AND IMPROVED "SUMNER" METHOD, 

LATITUDES . 90 N. TO 90 S. 

DECLINATIONS . -90 N. TO 90 S. 

Azimuths through Tables A, B. and C (or separately through Table D), for all the Heavenly Bodies 
at any Time the Body is above the Horizon ; and Great-circle Sailing-courses between any two 
Places on the Globe. 

Also other useful Navigational Tables, with Numerous Examples of Double Altitudes, 
Equal Altitudes, Azimuths, Ac. 

BY H. S. BLACKBURNE (EXTRA MASTER), 

Principal Examiner of Masters and Mates in New Zealand, and Nautical Adviser to the Government 
[Fourth Edition, 1916]. PRICE, 6S. 

MODERN UP-TO-DATE NAVIGATION. 

POSITION FINDING 

BY THE 

IMPROVED "SUMNER" METHOD 

CONTRASTED WITH , 

THE NEW NAVIGATION (Marcq St. Hilaire System) 
and the OLD " SUMNER " METHOD, 

TOGETHER WITH 

A few Special Star Reduction and Azimuth Tables. 



BY H. S. BLACKBURNE. 
PRICE, 1s. 60. 



BOOK OF " SUMNER' CHARTS. 

PRICE, 2s. 60. 

A book containing examples of positions found by the improved " Sumner " method 
from ex-meridians, and twenty-four plane blank " Sumner " charts on a convenient 
scale for facilitating the " Sumner " problem in connection with Captain Blackburne's 
A, B, and C azimuth tables mentioned above. 

Every single chart is available for any latitude through the aid of the above-men- 
tioned tables, by which greater accuracy of position is found, as well as a wider range for 
observation, than is given by the usually taught " Sumner's " method. 

NOTE. With reference to the above, Lieutenant G. W. Logan, United States Navy, 
editor of a previous revised edition of Bowditch's " American Practical Navigator," states 
that " the plane chart for plotting the intersection of ' Sumner ' lines is excellent, and 
I freely concede that your method by means of Table C 2 is an improvement on my own 
for those who work ' Sumner's ' with one position and an azimuth. U.S.S. ' Castine,' 
Santo Domingo City, S.D., 17th January, 1905." 

Mr. H. B. Goodwin, R.N., M.A., author of several works on navigation, &c., 
formerly Examiner in Nautical Astronomy at the Royal Naval College, Greenwich, 



" I notice several interesting features in your present edition, notably the adaptation 
of 'Sumner' methods to plane charts, which should be more generally known." 
Aug., 1905. __ 

PUBLISHED BY MARINE DEPARTMENT, NEW ZEALAND GOVERNMENT, WELLINGTON, NEW ZEALAND 

SOLD IN NEW ZEALAND AT THE SHIPPING OFFICES, AND BY BOOKSELLERS. 
SOLE AGENTS IN UNITED KINGDOM: JAMES BROWN AND SON, 52-58 DARNLEY STREET, GLASGOW. 



175 

EXTRACTS FROM PRESS REVIEWS 

ON THE 

Tables for Azimuths, Great - circle Sailing, 

AND 

REDUCTION TO THE MERIDIAN. 



[Prom the Syren and Shipping, 23rd August, 1905, and 4th November, 1908.] 
Captain Blackburne's labour-saving aids for navigators are known all over the 
world by his brethren who keep themselves posted in up-to-date methods ; and this 
collection of tables now published leaves nothing to desire by the navigator wishful of 
finding his ship's geographical position, or the error of her compass, with the least 
possible chance of error, and in the shortest possible interval of time, anywhere within 
the usual limits of navigation. There is one point in connection with these tables 
which is deserving of the close consideration of the Board of Trade. Although the 
practical seaman will almost invariably use such data at sea, yet the Board compels 
the candidates for certificates to plod along in a way which gives admittedly erroneous 
results under certain conditions. . . . That the Board of Trade should examine 
along one line that of antiquity and that practical navigators should work along 
quite another line that of labour-saving tables is surely ludicrous. The New 
Zealand Government requested the Board of Trade to allow the use in the examination- 
room of tables like those of Captain Blackburne's, together with improved methods of 
working, but the request has not been granted. We sincerely trust that the Board of 
Trade will see fit to adopt modern methods by allowing the candidates permission bo 
use the A, B, C Azimuth Tables of Blackburne, or any similar labour-saving work. 
More convenient in form or more utilitarian in application these tables could not be. 

[Extract from the Nautical Magazine, September and December, 1908.] 
In the new edition of his well-known A, B, C, and D Tables, Captain Blackburne 
must surely have cut all existing records. . . . Captain Blackburne is as inde- 
fatigable as ever in his efforts to lighten the labours of those who go down to the 
sea in ships. Early in the present year he published an edition of the A, B, and C 
Tables. They are now republished, with an appendix entitled Ex-meridian and 
Azimuth Inspection Tables. . . . The author seems here to have hit upon a 
happy idea, for we have a maximum of information in a minimum of space ; and, as 
he points out, once calculated, the reduction and azimuths will hold good for a long 
series of years. 

[Extract from the Shipping World, 9th December, 1908.] 

The new issue of his A, B, and C Tables for Azimuth, &c., is undoubtedly the 
most complete and comprehensive volume on this subject yet published. . . . 

[Extract from the United Service Magazine, December, 1908.] 
These tables now make it possible to determine the position of the ship more readily 
at any time, and with less trouble than ever before. 

[Extract from the Mariner, 15th December, 1908.] 

Sufficient is it to say that the various navigation tables, rules and examples, including 
a new and improved " Sumner " method, make the volume on all counts one of the most 
complete and authoritative that we know in nautical literature. 

[Extract from Shipping Illustrated, New York, 5th December, 1909.] 
These tables, as set forth in the present edition, are the most complete and com- 
prehensive Azimuth and Ex-meridian Tables for practical work yet published. 

[Extract from New Zealand Military Journal, October, 1913.] 
As an adjunct to marching or flying by day and night without a compass may 
be taken another work for the reason that the tables it contains practically enabled a 
revolution to be made in the old methods of night marching. This is "Tables for 
Azimuths and Great-circle Sailing," by H. S. Blackburne. 

Inset Azimuth. 



176 

EXTRACTS FROM LETTERS TO THE AUTHOR 



RE THE 



TABLES FOR AZIMUTHS AND REDUCTION TO THE MERIDIAN. 



Mr. W. H. SWENY, Chief Officer, P. and 0. s.s. " Mooltan," writes, 
I have now had your new edition of Azimuth and Reduction to the Meridian 
Tables in use for one Australian voyage, using them almost daily for stellar observation. 
The results obtained have been surprising, and so satisfactory that I have discarded all 
other books on these problems. 23rd January, 1909. 

Captain JOHN OWEN, Teacher of Navigation, Cardiff, writes, 
Your method of solving the Time Azimuth problem by the A, B, C Tables is concise, 
and easy of solution. If these tables were more generally known I think seafarers would 
use them in preference to Burdwood's or any other special tables employed at present. 
25th January, 1909. 

Mr. JOHN BLENCOWE, late Second Officer, B.I. s.s. " Shirala," writes, 
In Lyttelton I obtained a copy of your new Azimuth and Ex-meridian Tables, and 
on showing them to my brother officers they were so taken with them that they all bought 
a copy for themselves. I think the tables are splendid, and for the sake of the profession 
will do all I can to make them more widely known. 9th February, 1909. 

Captain P. THOMPSON, late Secretary to the Local Marine Board, and Examiner of 
Masters and Mates, London ; Author of " Navigation Simplified," &c., writes, 
Having gone carefully through your book I am satisfied that your short methods 
of solving the most practical problems in navigation will commend themselves to the 
officers of the Mercantile Marine ; for myself, I cannot too strongly express how highly 
I appreciate what you have done to simplify the every-day calculations of those navi- 
gators whose duties in the ordinary work of a steamer leave them little leisure for work- 
ing out a ship's position by the longer methods expected from them when undergoing 
the Board of Trade examination for a qualifying certificate. 12th February, 1909. 

Mr. S. 0. WARNER, Chief Officer, P. and O. s.s. " Socotra," writes, 
I should like to add my humble testimonial to the new A, B, C book you have 
brought out, and to tell you how much it is appreciated here on board. I certainly 
think it is the very best book of navigation ever printed. 13fch September, 1910. 

Captain GEORGE BURTON, Instructor of Cadets, Ocean Training-ship "Port Jackson," 

writes, 

I have shown your book to all our senior cadets, and advised them to procure 
copies. The book is certainly altogether the most complete education in modern 
navigation yet published. - 26th November, 1910. 

Captain HERBERT H. EDMONDS, Teacher of Navigation, Sydney, Australia, writes, 
Of the two systems the Marcq-Hilaire and that which you so strongly advocate I 
decidedly prefer the latter. ... I like your Ex-meridian Tables ; it is no extra 
work finding the azimuth beforehand, since it is required in the after-plotting. It is 
a great pity the Board of Trade do not keep abreast of the times in adopting this 
system. 17th December, 1910. 

Captain J. KING DAVIS, commanding the Australasian Antarctic Expedition, 
S.Y. " Aurora," writes, 

Macquarie Island, 16th December, 1911. 

We have already several copies of the previous edition, as I use nothing else, and 
have insisted on my officers learning to use them, as they are the only suitable tables 
for our work, and are much handier, in my opinion, for any latitude. 



177 



Mr. H. ROCHFORD HUGHES, Navigating Officer, H.M. Cable Steamer ''Iris," writes, 

Having just returned from Sydney, New South Wales, after sounding proposed 
track for the new cable from Auckland to that port, I hasten to write to say what 
a boon your splendid A, B, G Tables have proved during the expedition, more 
especially the C 2 Table. ... I have tried "new navigation" methods, and all 
the principal tables of the day, during my search for the shortest and most accurate 
methods, and have come to the conclusion that for our work your tables and system 
generally are the best. 5th and 8th February, 1912. 



Commander RICHARD HYDE, R.N., Navigation School, Portsmouth, writes, 

I have just returned from a cruise with our gunboats the " Dryad " and " Harrier," 
when I used your tables exclusively for finding azimuths, and personally I prefer them 
to Burdwood or Weir's diagram. 12th April, 1912. 



Lieutenant EDWARD R. G. R. EVANS, R.N., who Commanded the British Antarctic 
Expedition R.Y.S. " Terra Nova " from England to Antarctic in 1910, writes, 
I shall endeavour to bring your tables into more general use in the Navy, as I 
consider them facile princeps of their kind. Burdwood and Davis are so cumber- 
some. I think you will be pleased to hear that on the southern journey I used your 
tables exclusively, and worked out all magnetic variations and true bearings by means 
of them up to latitude 85 and hence to 88 almost by exterpolation. 17th April, 1912. 



Captain L. B. BENNETT GILLMAN, s.s. " Matatua," writes, 

Before leaving Wellington on our last homeward voyage I procured a 1911 edition 
of your tables for azimuth and reduction to the meridian. I think it is the cheapest 
and best book on practical navigation ever offered to the seafaring community. Had 
the price been two guineas instead of six shillings it would have been nearer the 
intrinsic value of the book. The tables are absolutely the last word in modern and 
up-to-date navigation. 30th April, 1912. 



Lieutenant HARRY PENNELL, R.N., Commanding the British Antarctic Expedition 

R.Y.S. " Terra Nova," writes, 

I have used your A, B, C and Ex-meridian Tables whenever the " Terra Nova" has 
made a voyage south, and have found them invaluable. In parts of Ross Sea the 
variation changes 1 for every four miles run at right angles to the lines of equal 
variation, and the large number of azimuths that it is necessary to take during the 
twenty-four hours would mean a prohibitive amount of work if your all embracing 
tables were not at hand. 3rd June, 1912. 



Captain THOMAS LIDDLE, Sunderland, writes, 

Your last 1911 edition is undoubtedly the best book published for navigators, and 
the cheapest. 28ih December, 1912. 



Lieut. -Col. W. A. TILNEY, commanding 17th Lancers, Sialkot, India, writes, 
Your tables have practically enabled us to revolutionize night marching, as you 
see by the enclosed report. 29th July, 1913. 

Lieut. E. BALLARD DALBY, R.N.R., Extra Master (London), H.M.S. "Carmania," 

at sea, writes, 

The officers who joined this ship in Liverpool when she was converted into an 
armed cruiser were drawn from nearly every company under the British flag, and no 
less than six of them had brought copies of your A and B Tables with them. It is a 
significant fact that once an officer commences to use them he never goes back to 
Burwood and Davis, where interpolation is in many cases tedious. Your tables 
certainly are the tables par excellence for an officer of the watch. 10th May, 1915. 



178 
EXTRACTS FROM PAPER REVIEWS 

AND LETTERS ON 

MODERN UP-TO-DATE NAVIGATION. 



[The Nautical Magazine, Glasgow, July, 1914.] 

One advantage that should accrue to this little book and to all those who use it is 
the fact that its editor and compiler, in addition to being a good theoretical man, is also 
an experienced navigator and practical shipmaster. Having spent some time in prepar- 
ing candidates for the Board of Trade examinations, he has acquired the " knack " of 
putting things as men can understand them, and in a way in which they will be most 
useful to them. The book throughout shows a sound knowledge of the subject, and 
will, with the help of the worked examples and chartlets, surely be the means of a 
larger number of navigators becoming interested in modern up-to-date navigation. 

[The United Service Gazette, London, 15th October, 1914.] 

The book contains some nautical tables of great value for ready position- finding 
from observations of two stars out of the meridian. They also give by simple 
inspection the true bearing within certain limits of a few bright stars, and the calculated 
reduction to the meridian up to about an hour or a little over from the meridian, 
enabling a navigator to determine his latitude and position-line from a single observa- 
tion of a star, with little more trouble than when the star is on the meridian. The 
book also contains several fully worked-out examples showing the use of the tables, 
with some well executed diagrams illustrating the problems ; the different methods of 
determining the ship's position by the " Old Sumner Method," the " Improved Sum- 
ner Method," and the " New Navigation Method " are contrasted, and the author 
clearly exposes some of the fallacious claims which have been made by one or two 
recent writers for the so-called "New Navigation" or "Marcq St. Hilaire" system 
of dealing with observations for position-finding. The value of the below Pole reduc- 
tion and Azimuth Tables is well illustrated by the example on page 47. Small as the 
work is, having been printed on thin paper, it contains the tabulated results of about 
19,900 calculations. 



Captain H. H. EDMONDS, Teacher of Navigation, Sydney, writes, 

I thoroughly endorse all you say on the Marcq St. Hilaire method; it is the truest 
thing that has been written on the subject. 

Captain T. L. EVANS, F.R.G.S., Manager, Donald Steamship Company, Bristol, writes, 

I am convinced that the book " Modern Up-to-date Navigation " is one of the 
best auxiliaries to the navigator that I have yet perused, and would have been glad 
of such a book during my career as master in the foreign service. I must congratulate 
you on the very excellent methods which you have published in your book, which I 
consider most valuable to all navigators who wish to ascertain the position of their ship, 
by the splendid methods contained in your book, and which are so simply illustrated 
and explained that any one with an ordinary amount of intelligence can grasp without 
any instructions except that which is contained in your book. I shall certainly have 
the greatest pleasure in recommending it to all my younger friends who are now masters 
and officers of ships. 

Captain THOS. LIDDLE, Sunderland, writes, 

It's wonderful the information you have got in such a small space, and so far I have 
never seen any book to equal it. Why the Board of Trade will not sanction the use 
of your books for the examinations I cannot understand. 

Captain J. W. MAXWELL, King Edward VII Nautical School, London E, writes, 

I agree with your remarks, and see in this little work how very clear and sound 
your knowledge is. 



179 
NEW ZEALAND 

NAUTICAL ALMANAC & TIDE-TABLES: 

ALSO 

Information with Plans about the Principal 
Ports of New Zealand, 

AND 

SUPPLEMENTARY INFORMATION TO DATE RELATING TO THE 
"NEW ZEALAND PILOT," EDITION 1908. 



Published by Direction of the, Hon. the Minister of Marine, Wellington, N.Z. 



PRICE - - 3/-. 



The above-mentioned work is published annually towards the end of the year 
for the following year. It contains the usual Nautical Almanac data required 
in the ordinary navigation of ships, tide-tables (calculated by the N.Z. Lands and 
Survey Department), giving time and heights of high and low water at Wellington 
and Auckland, as standard ports, and constants to about eighty other places in the 
Dominion ; also the tidal stream predictions for Tory Channel and French Pass, 
where the tidal streams attain a rate of five to seven knots at springs. Next to the 
tide-tables the special purpose of the work is to supplement and keep the " New 
Zealand Pilot " up to date, by collating all the notices to mariners and latest 
information since the last edition of the " New Zealand Pilot." It also gives 
somewhat fuller information, with plans of wharves, &c., about all the ports of any 
importance in the Dominion. 

The last edition of the work contains about 530 pages, and over thirty folded 
maps and plans of harbours, wharves, &c., with latest alterations, and much 
information relating to the principal ports and harbours of New Zealand and of 
value to mariners. 

Courses and distances between all the principal ports in New Zealand, also 
between New Zealand, Australia, Fiji, South Africa, San Francisco, Vancouver, 
Valparaiso, Panama, New York, and to England, via Cape Horn, and Panama, 
with the return via Capetown, are given in the work. 

Some very valuable nautical tables and examples of problems worked by 
their aid are published in the Almanac, which it is hoped will greatly encourage 
masters and officers generally to make a practice of determining the ship's position 
from two stars at twilight, as these tables make the problems very easy, and also 
enable the observer to make sure that he is taking the right star by the easy 
calculation of the approximate altitude, and the bearing of the stars is given at 
sight. 

The Almanac now finds its way not only to England and Australia^ but has 
been sent for from North America and Jamaica. Mr. G. H. Halligan, Inspecting 
Engineer and Hydrographer in New South Wales, wrote of a previous year's 
edition, " This most valuable publication is now almost indispensable in Australia, 
and I find it of the utmost value in my hydrographic investigations." 

The Editor of the " Rudder " Magazine, New York, U.S.A., wrote to the 
Secretary, Marine Department, when acknowledging receipt of a copy, " I am 
always pleased to receive this publication, and congratulate you on its excellence. 
It is far better than anything we have published in this country." 

PUBLISHED BY MARINE DEPARTMENT, N.Z. GOVERNMENT, WELLINGTON, N.Z. 

Sold in New Zealand at the Shipping Offices and Customhouses, and can be obtained in 
United Kingdom from the New Zealand High Commissioner, Victoria Street 
London, S.W- 



180 



Over 400 Pages of 
Solid Figure Matter. 



LARGE 
BOOK OF 



Over 400 Pages of 
Solid Figure Matter. 



NAUTICAL TABLES. 



Calculated Hour-angles and Altitude Azimuth Table, 

3O N. to 3O S.; 

Ex-meridian Tables, 6O N. to 6O S. ; and 

Calculated Reduction and Azimuths of 27 Bright 

Stars from 1 to 3 Hours from Meridian, 64 N. 

to 60 S. 



H. S. BLACKBURNE, 

Extra Master (London), 

PRINCIPAL EXAMINER OF MASTERS AND MATES IN NEW ZEALAND 
AND NAUTICAL ADVISER TO THE GOVERNMENT. 

Price : 7/6 in United Kingdom and 8/- in New Zealand. 

NOTHING has ever before been published to so quickly, simply, 
and accurately solve the problem of finding the ship's position from 
two or three stellar observations out of the meridian, or for deter- 
mining the latitude and position-line from a single observation, 
which may often be used in conjunction with a sounding, or the 
bearing of some mountain peak, or light, in determining the actual 
position of a ship. 

AZIMUTHS from stars within the limits of the table are more 
simply found than by any other tables, and without question the 
same thing may be said about the star REDUCTIONS which have 
been calculated for 27 of the brightest stars from about i hour from 
upper meridian and from 2 to 3 hours from the meridian below the 
Pole for the circumpolar stars, for the actual declination of the stars 
for the year 1920, and for latitudes between 64 N. and 60 S. The 
reduction and azimuth of star Polaris is given up to 6 hours above 
and 6 hours below the Pole. 

The great advantage of these tables for daylight and twilight 
observations is that the ready determination of the altitude and 
azimuth from the table prevents the possibility of the wrong star 
being taken, and an observation may be obtained by setting the 
approximate altitude to the sextant before the star is visible to the 
naked eye. 



CAPTAIN WALTER LUMSDEN, C.V.O., R.N., Director Royal Indian Marine, writes, saying : 
'I am obtaining copies of this publication for supply to Royal Indian Marine seagoia* vessels." 



i_i 

V 



The P. and O.S.N. Company, the N.Z.S.S. Company, the White Star Line, and 
the U.S.S. Company of New Zealand supply copies of the work to their steamers. 
The New Zealand Government are also supplying each of H.M.N.Z. transport 
steamers with a copy of the book. 

AGENTS IN UNITED KINGDOM: 

Thomas Ainsley, south Shields, England ; James Brown and Son, Glasgow, 
Scotland ; J. D. Potter, 145 Wineries, London E.G., England. 

SOLD BY NAUTICAL BOOKSELLERS AND AT THE GOVERNMENT SHIPPING 
OFFICES IN NEW ZEALAND. 



181 

EXTRACTS FROM PRESS REVIEWS AND LETTERS 

ON 

TABLES OF CALCULATED HOUR-ANGLES 

AND 

ALTITUDE AZIMUTH TABLE, ETC. 



[Extract from Shipping Illustrated, New York, U.S.A., April 3rd, 1915.] 

The main purpose of these tables is to make as easy as possible the problem of 
finding the ship's position from combined altitudes of the sun, moon, or stars, and 
especially to facilitate the much-neglected practice of determining the ship's position 
from two or three stars at twilight, a few minutes before sunrise, and a few minutes 
after sunset. By the aid of the calculated star reduction and azimuth tables in this 
book a latitude and position line can be obtained at any time when the stars are 
visible almost as easily as by meridian altitude of a star. This method is the simplest 
yet brought forth for quickly and accurately solving the problem of determining position 
from stellar observations out of the meridian, or for determining latitude and position 
line from a single observation, which may be used in connection with a sounding, or 
the bearing of some mountain peak or light. 

Captain G. N. TOMLIN, R.N., H.M.S. " Agincourt," writes," I have already found 
your tables most useful and simple ; I hope they will meet with the success they 



Commander HARRY PENNELL, R.N., H.M.S. "Duke of Edinburgh," writes, " These 
hour-angle and azimuth tables reduce sights now to the minimum of work conceivable 
when they fall within its limits. . . . 

Captain THOS. WASHINGTON, U.S. Navy, Hydrographer, writes, " I am sure your 
tables are going to prove to be a most useful and accurate help for shipmasters and 
others interested in navigation ; I congratulate you upon the excellence of the work." 

Captain HERBERT H. EDMONDS, Teacher of Navigation, Sydney, writes," Received 
my copy of your book with which I am greatly pleased. I have tested a few critical 
cases and find results all that can be desired, both with hour-angle and azimuths. What 
a boon to have all you want with a position-line in one act." 

Commander EDWARD R. G. R. EVANS, R.N., H.M.S. "Viking," writes, "Very 
many thanks for ' Tables of Calculated Hour-angles, Star Reductions, and Azimuth 
Tables.' Like all your works this is excellent, and simple enough for any navigator 
who will read the explanation and work a few examples until he is familiar with their 
use then they are a pleasure." 

Lieut. E. B. DALBY, R.N.R., H.M.S. " Carmania," writes, " I have purchased 
a copy of your new book, and hasten to say how much I like it. The printing is good, 
the arrangement could not be bettered, the explanations are copious, and the whole 
book a marvel of cheapness. I have checked the hour-angles in Table 1 by working 
out quite a number of sights in the usual way and then working the same sights by 
this table. In no case did I get a difference of over a second, and in most cases the 
error was under half a second. The facility and accuracy with which the azimuth is 
obtained through the latitude variation (with a little mental interpolation in some 
cases) is certainly remarkable. For your star reduction and azimuth tables I have 
nothing but admiration. For stellar navigation / know of nothing to equal these incom- 
parable tables." 

Captain ROBERT W. FERGUSON, of Brisbane, Queensland, writes, " The tables are 
magnificent, and the most singular part of them is the truly graphic Altitude Azimuth 
Table No. IV, it being the best aud most ingenious I have ever seen. . . . These 
and your ' Tables for Azimuth, Great-circle Sailing, and Reduction to the Meridian' 
90 N. to 90 S. are of inestimable value to the science of navigation, and your methods 
supersede all others in accuracy and brevity, for whioh you deserve well and worthily 
at the hands of the profession." 



Authority: MARCUS F. MABKS, Government Printer, Wellington, 1916. 



[Extract from N.Z. Gazette No. 103, 14th Sept., 1916.] 

Notice to Mariners No. 74 of 1916. 
NEW EDITION OF NAUTICAL TABLES PUBLISHED. 



Marine Department, 
Wellington, N.Z., llth September, 1916. 

NOTICE is hereby given that the New Zealand Marine 
Department have just published a fourth edition of 
" Tables for Azimuth, Great Circle Sailing, and Reduction 
to the Meridian," Lats. 90 N. to 90 S. 

The azimuth tables, which for some years have been acknow- 
ledged to be the most complete and comprehensive azimuth 
tables published, remain the same as in last edition. They 
include limits from pole to pole for sun, moon, and all the 
stars in the heavens, for any hour angle from the meridian. 

The reduction tables, though still very compact, have been 
more than doubled in size since issue of last edition, and their 
limits of use have been considerably enlarged. They are 
available for all latitudes and declinations, and for any alti- 
tude, often with more than double the hour- angle limits from 
the meridian given in the ex-meridian tables in the standard 
works of navigation in general use. 

They are also available for below pole hour-angles as well 
as the hour-angles from upper meridian. As an illustration 
of the wide limits of these tables an example is given on page 
158, which will no doubt surprise navigators generally. The 
position of ship is accurately determined from two ex-meridian 
latitudes where the reduction to both zenith distances was 
over 9, hour-angles over 1 h. 40 m., and azimuth over 40 
from the meridian. 

The accuracy of resulting position from these observations 
is proved by a fresh calculation of two longitudes from a near 
parallel of latitude, by the ordinary double altitude method, 
with the use of the A and B Tables. Other new and inter- 
esting problems have also been added in this edition. 

Published by Marine Department, New Zealand Govern- 
ment, Wellington, New Zealand. Price 6s. 

Sold in New Zealand at the shipping offices and by book- 
sellers. Sole agents in United Kingdom : James Brown and 
Son, 52-58 Darnley Street, Glasgow, Scotland. 

GEORGE ALLPORT, 

Secretary. 



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